Glasses having non-frangible stress profiles

ABSTRACT

A glass exhibiting non-frangible behavior in a region where substantially higher central tension is possible without reaching frangibility is provided. This region allows greater extension of the depth of compression in which fracture-causing flaws are arrested, without rendering the glass frangible despite the presence of high central tension region in the sample.

This application claims the benefit of priority under 35 U.S.C. §119 ofU.S. Provisional Application Ser. No. 62/014,372, filed on Jun. 19,2014, the content of which is relied upon and incorporated herein byreference in its entirety.

BACKGROUND

The disclosure relates to strengthened glass. More particularly, thedisclosure relates to strengthened glasses that do not exhibit frangiblebehavior.

Chemically strengthened glass is widely used as cover glass for mobiledevices, touch-enabled displays, and the like. In general, non-frangibleion exchanged glass is preferred as a cover glass for touch-screendevices in order to reduce the risk of user injury from small glasspieces due to self-accelerating highly fragmented fracture that ischaracteristic of highly-frangible stress conditions. Such conditionsare often produced as a result of combinations of excessive compressivestress and center tension in the sample. Recently disclosed criteria fornon-frangibility based on a thickness-dependent maximum center tension(CT) are valid for relatively small thicknesses (i.e., <0.8 mm) only inthe regime when the depth of the compressive layer (DOL) achieved bychemical strengthening is substantially smaller than the samplethickness.

SUMMARY

A glass exhibiting non-frangible behavior in a region wheresubstantially higher central tension is possible without reachingfrangibility is provided. This region allows greater extension of thedepth of compression in which fracture-causing flaws are arrestedwithout rendering the glass frangible despite the presence of a highcentral tension region in the sample.

Strengthened glasses that have deep compressive layers and do notexhibit frangible behavior (i.e., the glasses are non-frangible) areprovided. The glasses have surface compressive layers extending from thesurface to a depth of compression DOC that is at least about 8% (0.08t,where t is the thickness of the glass) of the total thickness of theglass, and a compressive stress CS and physical central tension CT,wherein CT−CS≦350 MPa, which, when applying the convention normally usedin the art (i.e., compression is expressed as a negative (<0) stress andtension is expressed as a positive (>0) stress), may be alternativelyexpressed as |CT|+|CS|≦350 MPa.

Accordingly, one aspect of the disclosure is to provide a glass having acompressive layer extending from a surface of the glass to a depth ofcompression DOC and under a maximum compressive stress CS, a centralregion having a maximum physical central tension CT at a center of theglass, the central region extending outward from the center to the depthof compression, and a thickness t in a range from about 0.3 mm to about1.0 mm, wherein DOC≧0.08·t and CT−CS≦350 MPa or, alternatively,|CT|+|CS|≦350 MPa.

A second aspect of the disclosure is to provide a glass having acompressive layer extending from a surface of the glass to a depth ofcompression DOC and under a maximum compressive stress CS, a centralregion having a maximum physical central tension CT at a center of theglass, the central region extending outward from the center to the depthof compression into the glass, and a thickness t in a range from about0.3 mm to about 1.0 mm. The depth of compression DOC is greater than orequal to 0.08·t and the glass has an average elastic energy density ofless than about 200 J/m²·mm.

A third aspect of the disclosure is to provide a glass comprising: acompressive layer extending from a surface of the glass to a depth ofcompression DOC, the compressive surface layer having a maximumcompressive stress CS; a central region having a maximum physicalcentral tension CT at a center of the glass. The central region extendsoutward from the center of the glass to the depth of compression. Theglass has a thickness t in a range from about 0.3 mm to about 1.0 mm,wherein DOC≧0.08·t and CT−CS≦350 MPa or, alternatively, |CT|+|CS|≦350MPa. The physical central tension CT is greater than0.631×(57−9.0×ln(t)+49.3×(ln(t))²) when 0.3 mm≦t≦0.5 mm. The physicalcentral tension CT is greater than 0.728×(57−9.0×ln(t)+49.3×(ln(t))²)when 0.5 mm≦t≦0.7 mm. The physical central tension CT is greater than

$0.755 \times \left( {{{- 38.7}\left( \frac{MPa}{mm} \right) \times {\ln (t)}({mm})} + {48.2({MPa})}} \right){MPa}$

when 0.7 mm<t≦1.0 mm.

A fourth aspect of the disclosure is to provide a glass comprising: acompressive layer extending from a surface of the glass to a depth ofcompression DOC, the compressive surface layer having a maximumcompressive stress CS; a central region having a maximum physicalcentral tension CT at a center of the glass, the central regionextending outward from the center of the glass to the depth ofcompression, wherein the glass has an average elastic energy density ofless than 200 J/m²·mm; and a thickness t in a range from about 0.3 mm toabout 1.0 mm, wherein DOC≧0.08·t. When 0.3 mm≦t≦0.5 mm, the physicalcentral tension CT is greater than 0.681×(57−9.0×ln(t)+49.3×(ln(t))²)MPa. When 0.5 mm≦t≦0.7 mm, the physical central tension CT is greaterthan 0.728×(57−9.0×ln(t)+49.3×(ln(t))²) MPa, and when 7 mm<t≦1.0 mm, thephysical central tension CT is greater than

$0.755 \times \left( {{{- 38.7}\left( \frac{MPa}{mm} \right) \times {\ln (t)}({mm})} + {48.2({MPa})}} \right){{MPa}.}$

These and other aspects, advantages, and salient features will becomeapparent from the following detailed description, the accompanyingdrawings, and the appended claims.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic cross-sectional view of a chemically strengthenedglass article;

FIG. 2 is a plot of the ratio of the approximate adopted CT_(A) and thecalculated physical central tension CT (CT(erfc)) for the error function(erfc) profile characteristic of linear diffusion;

FIG. 3 is a plot of the frangibility limit CT in terms of CT₁;

FIG. 4 is a plot of the frangibility limit CT in terms of CT₃;

FIG. 5 is a plot of transverse magnetic (TM) and transverse electric(TE) index profiles extracted by the IWKB-based algorithm via prismcoupling measurements;

FIG. 6 is a plot of a stress profile for a 0.4 mm thick glass that wasexchanged 17.7 hours at 440° C. in a bath containing 50% NaNO₃ and 50%KNO₃ by weight;

FIG. 7 is a plot of an example of the stress profile extracted using theIWKB method;

FIG. 8 is a plot of the stress profile for double-ion exchanged 0.55mm-thick glass;

FIG. 9 is a plot of TE and TM index profiles of the double-ion-exchangedglass sample of FIG. 8;

FIG. 10 a is a photograph showing strengthened glass articles 1)exhibiting frangible behavior upon fragmentation; and 2) exhibitingnon-frangible behavior upon fragmentation; and

FIG. 10 b is a photograph showing strengthened glass sheets that exhibitnon-frangible behavior upon fragmentation.

DETAILED DESCRIPTION

In the following description, like reference characters designate likeor corresponding parts throughout the several views shown in thefigures. It is also understood that, unless otherwise specified, termssuch as “top,” “bottom,” “outward,” “inward,” and the like are words ofconvenience and are not to be construed as limiting terms. In addition,whenever a group is described as comprising at least one of a group ofelements and combinations thereof, it is understood that the group maycomprise, consist essentially of, or consist of any number of thoseelements recited, either individually or in combination with each other.Similarly, whenever a group is described as consisting of at least oneof a group of elements or combinations thereof, it is understood thatthe group may consist of any number of those elements recited, eitherindividually or in combination with each other. Unless otherwisespecified, a range of values, when recited, includes both the upper andlower limits of the range as well as any ranges therebetween. As usedherein, the indefinite articles “a,” “an,” and the correspondingdefinite article “the” mean “at least one” or “one or more,” unlessotherwise specified. It also is understood that the various featuresdisclosed in the specification and the drawings can be used in any andall combinations.

As used herein, the terms “glass article” and “glass articles” are usedin their broadest sense to include any object made wholly or partly ofglass. Unless otherwise specified, all compositions are expressed interms of mole percent (mol %).

It is noted that the terms “substantially” and “about” may be utilizedherein to represent the inherent degree of uncertainty that may beattributed to any quantitative comparison, value, measurement, or otherrepresentation. These terms are also utilized herein to represent thedegree by which a quantitative representation may vary from a statedreference without resulting in a change in the basic function of thesubject matter at issue. Thus, a glass that is “substantially free ofMgO” is one in which MgO is not actively added or batched into theglass, but may be present in very small amounts as a contaminant (i.e.,<0.1 mol %).

Referring to the drawings in general and to FIG. 1 in particular, itwill be understood that the illustrations are for the purpose ofdescribing particular embodiments and are not intended to limit thedisclosure or appended claims thereto. The drawings are not necessarilyto scale, and certain features and certain views of the drawings may beshown exaggerated in scale or in schematic in the interest of clarityand conciseness.

As used herein, the terms “depth of layer” and “DOL” refer to the depthof the compressive layer as determined by surface stress (FSM)measurements using commercially available instruments such as theFSM-6000.

As used herein, the terms “depth of compression” and “DOC” refer to thedepth at which the stress within the glass changes from compressive totensile stress. At the DOC, the stress crosses from a positive(compressive) stress to a negative (tensile) stress and thus has a valueof zero.

According to the convention normally used in the art, compression isexpressed as a negative (<0) stress and tension is expressed as apositive (>0) stress. Throughout this description, however, compressivestress CS is expressed as a positive or absolute value—i.e., as recitedherein, CS=|CS| and central tension or tensile stress is expressed as anegative value in order to better visualize the compressive stressprofiles described herein, unless otherwise specified.

Ion exchange is commonly used to chemically strengthen glasses. In oneparticular example, alkali cations within a source of such cations(e.g., a molten salt, or “ion exchange,” bath) are exchanged withsmaller alkali cations within the glass to achieve a layer that is undera compressive stress (CS) near the surface of the glass. For example,potassium ions from the cation source are often exchanged with sodiumions within the glass. The compressive layer extends from the surface toa depth within the glass and typically decrease from a maximum at thesurface to 0 at the depth of compression DOC.

In one embodiment, the strengthened glasses described herein have amaximum compressive stress of at least about 150 MPa and, in someembodiments, at least about 200 MPa. In certain embodiments, thecompressive stress is less than about 250 MPa.

A cross-sectional schematic view of an ion exchanged glass article isshown in FIG. 1. Glass article 100 has a thickness t, first surface 110,and second surface 112. While the embodiment shown in FIG. 1 depictsglass article 100 as a flat planar sheet or plate, the glass article mayhave other configurations, such as three dimensional shapes or othernon-planar configurations. Glass article 100 has a first compressiveregion 120 extending from first surface 110 to a depth of compression(DOC) d₁ into the bulk of the glass article 100. In the embodiment shownin FIG. 1, glass article 100 also has a second compressive region 122extending from second surface 112 to a second depth of compression (DOC)d₂. Glass article 100 also has a central region 130 that extends from d₁to d₂. Central region 130 is under a tensile stress or physical centraltension (CT), which balances or counteracts the compressive stresses ofregions 120 and 122. The depths d₁, d₂ of first and second compressiveregions 120, 122 protect the glass article 100 from the propagation offlaws introduced by sharp impact to first and second surfaces 110, 112of glass article 100, while the compressive stress minimizes thelikelihood of a flaw penetrating through the depth d₁, d₂ of first andsecond compressive regions 120, 122.

In some embodiments, the depth of compression DOC is at least about 8%of the total thickness t of the glass article—i.e., DOC≧0.8t—and, incertain embodiments, DOC≧0.8t when the thickness t is greater than 0.75mm. In other embodiments, the depth of compression DOC is at least about9% of the thickness t (DOC≧0.8t) and, in certain embodiments, DOC≧0.9twhen the thickness t is greater than 0.5 mm.

Compressive stress CS and depth of layer DOL are measured using thosemeans known in the art. Such means include, but are not limited to,measurement of surface stress (FSM) using commercially availableinstruments such as, for example, the FSM-6000 stress meter,manufactured by Luceo Co., Ltd. (Tokyo, Japan), or the like, and methodsof measuring compressive stress and depth of layer are described in ASTM1422C-99, entitled “Standard Specification for Chemically StrengthenedFlat Glass,” and ASTM 1279.19779 “Standard Test Method forNon-Destructive Photoelastic Measurement of Edge and Surface Stresses inAnnealed, Heat-Strengthened, and Fully-Tempered Flat Glass,” thecontents of which are incorporated herein by reference in theirentirety. Surface stress measurements rely upon the accurate measurementof the stress optical coefficient (SOC), which is related to thebirefringence of the glass. The SOC in turn is measured by those methodsthat are known in the art, such as fiber and four point bend methods,both of which are described in ASTM standard C770-98 (2008), entitled“Standard Test Method for Measurement of Glass Stress-OpticalCoefficient,” the contents of which are incorporated herein by referencein their entirety, and a bulk cylinder method.

The relationship between CS and physical central tension CT may, in someembodiments, be approximated by the expression:

CT=(CS·DOL)/(t−2DOL)  (1),

where t is the thickness, expressed in microns (μm), of the glassarticle. In various sections of the disclosure, central tensions CT andcompressive stresses CS are expressed in megaPascals (MPa), thickness tis expressed in either microns (μm) or millimeters (mm), and depth oflayer DOL is expressed in microns (μm).

For strengthened glass articles in which the compressive stress layersextend to deeper depths within the glass, the FSM technique may sufferfrom contrast issues, which affect the observed DOL value. At deeper DOLvalues, there may be inadequate contrast between the TE and TM spectra,thus making the calculation of the difference between TE and TMspectra—and determining the DOL—more difficult. Moreover, the FSMtechnique is incapable of determining the compressive stress profile(i.e., the variation of compressive stress as a function of depth withinthe glass). In addition, the FSM technique is incapable of determiningthe depth of layer resulting from the ion exchange of certain elementssuch as, for example, lithium.

The techniques described below have been developed to more accuratelydetermine the depth of compression (DOC) and compressive stress profilesfor strengthened glass articles.

In U.S. patent application Ser. No. 13/463,322, entitled “Systems AndMethods for Measuring the Stress Profile of Ion-Exchanged Glass(hereinafter referred to as “Roussev I”),” filed by Rostislav V. Roussevet al. on May 3, 2012, and claiming priority to U.S. Provisional PatentApplication No. 61/489,800, having the same title and filed on May 25,2011, two methods for extracting detailed and precise stress profiles(stress as a function of depth) of tempered or chemically strengthenedglass are disclosed. The spectra of bound optical modes for TM and TEpolarization are collected via prism coupling techniques, and used intheir entirety to obtain detailed and precise TM and TE refractive indexprofiles n_(TM)(z) and n_(TE)(z). The contents of the above applicationsare incorporated herein by reference in their entirety.

In one embodiment, the detailed index profiles are obtained from themode spectra by using the inverse Wentzel-Kramers-Brillouin (IWKB)method.

In another embodiment, the detailed index profiles are obtained byfitting the measured mode spectra to numerically calculated spectra ofpre-defined functional forms that describe the shapes of the indexprofiles and obtaining the parameters of the functional forms from thebest fit. The detailed stress profile S(z) is calculated from thedifference of the recovered TM and TE index profiles by using a knownvalue of the stress-optic coefficient (SOC):

S(z)=[n _(TM)(z)−n _(TE)(z)]/SOC  (2).

Due to the small value of the SOC, the birefringence n_(TM)(z)−n_(TE)(z)at any depth z is a small fraction (typically on the order of 1%) ofeither of the indices n_(TM)(z) and n_(TE)(z). Obtaining stress profilesthat are not significantly distorted due to noise in the measured modespectra requires determination of the mode effective indices with aprecision on the order of 0.00001 RIU. The methods disclosed in RoussevI further include techniques applied to the raw data to ensure such highprecision for the measured mode indices, despite noise and/or poorcontrast in the collected TE and TM mode spectra or images of the modespectra. Such techniques include noise-averaging, filtering, and curvefitting to find the positions of the extremes corresponding to the modeswith sub-pixel resolution.

Similarly, U.S. patent application Ser. No. 14/033,954, entitled“Systems and Methods for Measuring Birefringence in Glass andGlass-Ceramics (hereinafter “Roussev II”),” filed by Rostislav V.Roussev et al. on Sep. 23, 2013, and claiming priority to U.S.Provisional Application Ser. No. 61/706,891, having the same title andfiled on Sep. 28, 2012, discloses an apparatus and methods for opticallymeasuring birefringence on the surface of glass and glass ceramics,including opaque glass and glass ceramics. Unlike Roussev I, in whichdiscrete spectra of modes are identified, the methods disclosed inRoussev II rely on careful analysis of the angular intensitydistribution for TM and TE light reflected by a prism-sample interfacein a prism-coupling configuration of measurements. The contents of theabove applications are incorporated herein by reference in theirentirety.

Hence, correct distribution of the reflected optical intensity vs. angleis significantly more important than in traditional prism-couplingstress-measurements, where only the locations of the discrete modes aresought. To this end, the methods disclosed in Roussev 1 and Roussev IIcomprise techniques for normalizing the intensity spectra, includingnormalizing to a reference image or signal, correction for nonlinearityof the detector, averaging multiple images to reduce image noise andspeckle, and application of digital filtering to further smooth theintensity of angular spectra. In addition, one method includes formationof a contrast signal, which is additionally normalized to correct forfundamental differences in shape between TM and TE signals. Theaforementioned method relies on achieving two signals that are nearlyidentical and determining their mutual displacement with sub-pixelresolution by comparing portions of the signals containing the steepestregions. The birefringence is proportional to the mutual displacement,with a coefficient determined by the apparatus design, which includesprism geometry and index, focal length of the lens, and pixel spacing onthe sensor. The stress is determined by multiplying the measuredbirefringence by a known stress-optic coefficient.

In another method, derivatives of the TM and TE signals are determinedafter application of some combination of the aforementioned signalconditioning techniques. The locations of the maximum derivatives of theTM and TE signals are obtained with sub-pixel resolution, and thebirefringence is proportional to the spacing of the above two maxima,with a coefficient determined as before by the apparatus parameters.

Associated with the requirement for correct intensity extraction, theapparatus comprises several enhancements, such as using alight-scattering surface (static diffuser) in close proximity to or onthe prism entrance surface to improve the angular uniformity ofillumination, a moving diffuser for speckle reduction when the lightsource is coherent or partially coherent, and light-absorbing coatingson portions of the input and output facets of the prism and on the sidefacets of the prism to reduce parasitic background which tends todistort the intensity signal. In addition, the apparatus may include aninfrared light source to enable measurement of opaque materials.

Furthermore, Roussev II discloses a range of wavelengths and attenuationcoefficients of the studied sample, where measurements are enabled bythe described methods and apparatus enhancements. The range is definedby α_(s)λ<250πσ_(s), where α_(s) is the optical attenuation coefficientat measurement wavelength λ, and σ_(s) is the expected value of thestress to be measured with typically required precision for practicalapplications. This wide range allows measurements of practicalimportance to be obtained at wavelengths where the large opticalattenuation renders previously existing measurement methodsinapplicable. For example, Roussev II discloses successful measurementsof stress-induced birefringence of opaque white glass-ceramic at awavelength of 1550 nm, where the attenuation is greater than about 30dB/mm.

While it is noted above that there are some issues with the FSMtechnique at deeper DOL values, FSM is still a beneficial conventionaltechnique which may utilized with the understanding that an error rangeof up to +/−20% is possible at deeper DOL values. The terms “depth oflayer” and “DOL” as used herein refer to DOL values computed using theFSM technique, whereas the terms “depth of compression” and “DOC” referto depths of the compressive layer determined by the methods describedin Roussev I & II.

As stated above, the glass articles may be chemically strengthened byion exchange. In this process, ions at or near the surface of the glassare replaced by—or exchanged with—larger ions having the same valence oroxidation state. In those embodiments in which the glass articlecomprises, consists essentially of, or consists of an alkalialuminosilicate glass, ions in the surface layer of the glass and thelarger ions are monovalent alkali metal cations, such as Li⁺ (whenpresent in the glass), Na⁺, K⁺, Rb⁺, and Cs⁺. Alternatively, monovalentcations in the surface layer may be replaced with monovalent cationsother than alkali metal cations, such as Ag⁺ or the like.

Ion exchange processes are typically carried out by immersing a glassarticle in a molten salt bath containing the larger ions to be exchangedwith the smaller ions in the glass. It will be appreciated by thoseskilled in the art that parameters for the ion exchange process,including, but not limited to, bath composition and temperature,immersion time, the number of immersions of the glass in a salt bath (orbaths), use of multiple salt baths, and additional steps such asannealing, washing, and the like, are generally determined by thecomposition of the glass and the desired depth of layer and compressivestress of the glass that result from the strengthening operation. By wayof example, ion exchange of alkali metal-containing glasses may beachieved by immersion in at least one molten bath containing a salt suchas, but not limited to, nitrates, sulfates, and chlorides of the largeralkali metal ion. The temperature of the molten salt bath typically isin a range from about 380° C. up to about 450° C. or to about 460° C.,while immersion times range from about 15 minutes up to about 40 hours.However, temperatures and immersion times different from those describedabove may also be used.

In addition, non-limiting examples of ion exchange processes in whichglass is immersed in multiple ion exchange baths, with washing and/orannealing steps between immersions, are described in U.S. Pat. No.8,561,429, by Douglas C. Allan et al., issued on Oct. 22, 2013, entitled“Glass with Compressive Surface for Consumer Applications,” and claimingpriority from U.S. Provisional Patent Application No. 61/079,995, filedJul. 11, 2008, in which glass is strengthened by immersion in multiple,successive, ion exchange treatments in salt baths of differentconcentrations; and U.S. Pat. No. 8,312,739, by Christopher M. Lee etal., issued on Nov. 20, 2012, and entitled “Dual Stage Ion Exchange forChemical Strengthening of Glass,” and claiming priority from U.S.Provisional Patent Application No. 61/084,398, filed Jul. 29, 2008, inwhich glass is strengthened by ion exchange in a first bath is dilutedwith an effluent ion, followed by immersion in a second bath having asmaller concentration of the effluent ion than the first bath. Thecontents of U.S. Pat. Nos. 8,561,429 and 8,312,739 are incorporatedherein by reference in their entirety.

The compressive stress is created by chemically strengthening the glassarticle, for example, by the ion exchange processes previously describedherein, in which a plurality of first metal ions in the outer region ofthe glass article is exchanged with a plurality of second metal ions sothat the outer region comprises the plurality of the second metal ions.Each of the first metal ions has a first ionic radius and each of thesecond alkali metal ions has a second ionic radius. The second ionicradius is greater than the first ionic radius, and the presence of thelarger second alkali metal ions in the outer region creates thecompressive stress in the outer region.

At least one of the first metal ions and second metal ions are ions ofan alkali metal. The first ions may be ions of lithium, sodium,potassium, and rubidium. The second metal ions may be ions of one ofsodium, potassium, rubidium, and cesium, with the proviso that thesecond alkali metal ion has an ionic radius greater than the ionicradius than the first alkali metal ion.

Described herein are chemically strengthened glasses, such as CorningGorilla® glass, that are used as a cover glass for mobile electronicdevices and touch-enabled displays. In particular, development ofchemically strengthened glass focuses on stress profiles with greaterdepth of the compressive layer that help reduce the probability ofexplosive or frangible glass fracture when the device is dropped on ahard, rough surface. Such fracture ejects glass pieces with substantialkinetic energy due to self-accelerating, highly fragmented fracture thatis characteristic of highly-frangible stress conditions produced as aresult of combinations of excessive compressive stress and centraltension in the glass.

Frangible behavior is characterized by at least one of: breaking of thestrengthened glass article (e.g., a plate or sheet) into multiple smallpieces (e.g., 1 mm); the number of fragments formed per unit area of theglass article; multiple crack branching from an initial crack in theglass article; violent ejection of at least one fragment to a specifieddistance (e.g., about 5 cm, or about 2 inches) from its originallocation; and combinations of any of the foregoing breaking (size anddensity), cracking, and ejecting behaviors. As used herein, the terms“frangible behavior” and “frangibility” refer to those modes of violentor energetic fragmentation of a strengthened glass article absent anyexternal restraints, such as coatings, adhesive layers, or the like.While coatings, adhesive layers, and the like may be used in conjunctionwith the strengthened glass articles described herein, such externalrestraints are not used in determining the frangibility or frangiblebehavior of the glass articles.

Examples of frangible behavior and non-frangible behavior ofstrengthened glass articles upon point impact with a sharp indenter areshown in FIGS. 10 a and 10 b. The point impact test that is used todetermine frangible behavior includes an apparatus that is delivered tothe surface of the glass article with a force that is just sufficient torelease the internally stored energy present within the strengthenedglass article. That is, the point impact force is sufficient to createat least one new crack at the surface of the strengthened glass sheetand extend the crack through the compressive stress CS region (i.e.,depth of layer) into the region that is under central tension CT. Theimpact energy needed to create or activate the crack in a strengthenedglass sheet depends upon the compressive stress CS and depth of layerDOL of the article, and thus upon the conditions under which the sheetwas strengthened (i.e., the conditions used to strengthen a glass by ionexchange). Otherwise, each ion exchanged glass plate shown in FIGS. 10 aand 10 b was subjected to a sharp dart indenter (e.g., a SiC indenter)contact sufficient to propagate a crack into the inner region of theplate, the inner region being under tensile stress. The force applied tothe glass plate was just sufficient to reach the beginning of the innerregion, thus allowing the energy that drives the crack to come from thetensile stresses in the inner region rather than from the force of thedart impact on the outer surface. The degree of ejection may bedetermined, for example, by centering the glass sample on a grid,impacting the sample, and measuring the ejection distance of individualpieces using the grid.

Referring to FIG. 10 a, glass plate a can be classified as beingfrangible. In particular, glass plate a fragmented into multiple smallpieces that were ejected, and exhibited a large degree of crackbranching from the initial crack to produce the small pieces.Approximately 50% of the fragments are less than 1 mm in size, and it isestimated that about 8 to 10 cracks branched from the initial crack.Glass pieces were also ejected about 5 cm from original glass plate a,as seen in FIG. 10 a. A glass article that exhibits any of the threecriteria (i.e., multiple crack branching, ejection, and extremefragmentation) described hereinabove is classified as being frangible.For example, if a glass exhibits excessive branching alone but does notexhibit ejection or extreme fragmentation as described above, the glassis still characterized as frangible.

Glass plates b, c, (FIG. 10 b) and d (FIG. 10 a) are classified as notfrangible. In each of these samples, the glass sheet has broken into asmall number of large pieces. Glass plate b (FIG. 10 b), for example,has broken into two large pieces with no crack branching; glass plate c(FIG. 10 b) has broken into four pieces with two cracks branching fromthe initial crack; and glass plate d (FIG. 10 a) has broken into fourpieces with two cracks branching from the initial crack. Based on theabsence of ejected fragments (i.e., no glass pieces forcefully ejectedmore than 2 inches from their original location), there are no visiblefragments with a size of 1 mm or less, and the minimal amount ofobserved crack branching, samples b, c, and d are classified asnon-frangible or substantially non-frangible.

Based on the foregoing, a frangibility index (Table 1) can beconstructed to quantify the degree of frangible or non-frangiblebehavior of a glass, glass ceramic, and/or a ceramic article upon impactwith another object. Index numbers, ranging from 1 for non-frangiblebehavior to 5 for highly frangible behavior, have been assigned todescribe different levels of frangibility or non-frangibility. Using theindex, frangibility can be characterized in terms of numerousparameters: 1) the percentage of the population of fragments having adiameter (i.e., maximum dimension) of less than 1 mm (“Fragment size” inTable 1); 2) the number of fragments formed per unit area (in thisinstance, cm²) of the sample (“Fragment density” in Table 1); 3) thenumber of cracks branching from the initial crack formed upon impact(“Crack branching” in Table 1); and 4) the percentage of the populationof fragments that is ejected upon impact more than about 5 cm (or about2 inches) from their original position (“Ejection” in Table 1).

TABLE 1 Criteria for determining the degree of frangibility andfrangibility index. Degree Frangi- Fragment of bili- Fragment densityfrangi- ty size (fragments/ Crack Ejection bility index (% ≦1 mm) cm²)branching (% ≧5 cm) High 5 >20 >7 >9 >6 Medium 4 10 < n ≦ 20 5 < n ≦ 7 7< n ≦ 9 4 < n ≦ 6 Low 3  5 < n ≦ 10 3 < n ≦ 5 5 < n ≦ 7 2 < n ≦ 4 None 20 < n ≦ 5 1 < n ≦ 3 2 < n ≦ 5 0 < n ≦ 2 1 0 n ≦ 1 n ≦ 2 0

A frangibility index is assigned to a glass article if the article meetsat least one of the criteria associated with a particular index value.Alternatively, if a glass article meets criteria between two particularlevels of frangibility, the article may be assigned a frangibility indexrange (e.g., a frangibility index of 2-3). The glass article may beassigned the highest frangibility index value, as determined from theindividual criteria listed in Table 1. In many instances, it is notpossible to ascertain the values of each of the criteria, such as thefragmentation density or percentage of fragments ejected more than 5 cmfrom their original position, listed in Table 1. The different criteriaare thus considered individual, alternative measures of frangiblebehavior and the frangibility index such that a glass article fallingwithin one criteria level will be assigned the corresponding degree offrangibility and frangibility index. If the frangibility index based onany of the four criteria listed in Table 1 is 3 or greater, the glassarticle is classified as frangible.

Applying the foregoing frangibility index to the samples shown in FIGS.10 a and 10 b, glass plate a fragmented into multiple ejected smallpieces and exhibited a large degree of crack branching from the initialcrack to produce the small pieces. Approximately 50% of the fragmentsare less than 1 mm in size and it is estimated that about 8 to 10 cracksbranched from the initial crack. Based upon the criteria listed in Table1, glass plate a has a frangibility index of between about 4-5, and istherefore classified as having a medium-high degree of frangibility.

A glass article having a frangibility index of less than 3 (lowfrangibility) may be considered to be non-frangible or substantiallynon-frangible. Glass plates b, c, and d each lack fragments having adiameter of less than 1 mm, multiple branching from the initial crackformed upon impact and fragments ejected more than 5 cm from theiroriginal position. Glass plates b, c, and d are non-frangible and thushave a frangibility index of 1 (not frangible).

As previously discussed, the observed differences in behavior betweenglass plate a, which exhibited frangible behavior, and glass plates b,c, and d, which exhibited non-frangible behavior, in FIGS. 10 a and 10 bmay be attributed to differences in central tension CT among the samplestested. The possibility of such frangible behavior is one considerationin designing various glass products, such as cover plates or windows forportable or mobile electronic devices, including cellular phones,entertainment devices, and the like, as well as for displays forinformation terminal (IT) devices, such as laptop computers. Moreover,the depth of the compression layer DOL and the maximum value ofcompressive stress CS_(s) that can be designed into or provided to aglass article are limited by such frangible behavior.

Accordingly, the strengthened glass articles described herein, in someembodiments, exhibit a frangibility index of less than 3 when subjectedto a point impact sufficient to break the strengthened glass article. Inother embodiments, non-frangible strengthened glass articles may achievea frangibility index of less than 2 or 1.

Recently disclosed criteria for non-frangibility based on athickness-dependent maximum physical central tension CT are valid forrelatively small thicknesses (i.e., t<0.8 mm) only in the regime whenthe depth of layer (DOL) of chemical strengthening is substantiallysmaller than the sample thickness t (i.e., DOL<0.1t). As describedherein, substantially higher central tension values than thosepreviously disclosed without reaching the frangibility limit of theglass are possible when the DOL comprises a larger proportion of theoverall thickness t. This additional region of non-frangibility allowsfurther extension of the depth of compression without rendering theglass frangible despite the development of high central tension withinthe sample. The increased depth of the compressive layer enables deeperfracture-causing flaws to be arrested.

In one aspect of the invention, an upper limit of the sum of CS and CTwhich allows an increase of DOL without reaching frangibility isdisclosed, including cases where the central tension CT increases verysubstantially above the most recently known CT frangibility limit,disclosed in U.S. Pat. No. 8,415,013, entitled “Strengthened GlassArticles and Methods of Making” by Kristen Barefoot et al. (referred tohereinafter as “Barefoot I”), issued on Apr. 9, 2013.

In one aspect, this upper limit of the sum of CS and CT is associatedwith an upper limit of the maximum spatial variation in K⁺ concentrationin a sample. This spatial variation that is obtained by a single-stepion exchange of K⁺ for Na⁺ in a glass substrate in which Na⁺, or Na⁺ andK⁺, are the only alkali ions in the glass.

In another aspect, an additional criterion for frangibility based ontotal stored elastic energy is introduced, allowing prediction offrangibility stress conditions in cases where the DOL is a substantialfraction of the sample thickness t. In one embodiment, DOL>0.1t and, inother embodiments DOL>0.15t. Under these conditions, frangibilityconditions are controlled for stress profiles obtained by eithersingle-step or two-step ion exchange. In addition, the total storedelastic energy criterion allows correct control of frangibility forstress profiles obtained by simultaneous or multi-step ion exchangeinvolving counter diffusion of more than two ions. The average elasticenergy is the total elastic energy divided by the thickness t of theglass article.

The total-elastic-energy criterion allows quick non-destructive qualitycontrol of frangibility based on stress measurements such as prismcoupling for single-ion exchange and compressive stress profilesobtained by double-ion exchange having large depths of layer.

Barefoot I describes the frangibility limit for glass thicknessessmaller than about 0.75 mm, where an extrapolation of an earlier-knownlinear dependence found for larger thicknesses underestimated the upperlimit of the non-frangible design space. “Nonlinear threshold centraltension CT₁” is given by the empirical formula

CT₁(MPa)≦−38.7(MPa)×ln(t)(mm)+48.2(MPa)  (3),

where t is the sample thickness. Based on proper dimensional analysis,ln(t), where t is expressed in mm, is dimensionless. The dimensions ofthe coefficient of the ln(t) term is actually megaPascals (MPa), and areexpressed as such. The CT measurement values that are compared to theabove formula are approximated by the equation

CT_(A)(CS,DOL,t)=(CS×DOL)/(t−2DOL)  (4).

The term CT_(A) signifies that the above approximation for finding CThas become accepted and widely used for process and quality control inthe field of chemically strengthened glass. According to Barefoot I, thefrangibility limit CT₁ ranges from 48.2 MPa for a substrate thickness of1 mm to 94.8 MPa for a thicknesses of 0.3 mm.

In U.S. patent application Ser. No. 14/405,041, filed Dec. 12, 2014, byKristen Barefoot et al., entitled “Strengthened Glass Articles andMethods of Making (referred to hereinafter as “Barefoot II”),” an evenhigher nonlinear frangibility CT_(A) limit is disclosed. Thefrangibility limit CT₃ is expressed as a function of thickness for thethickness range 0.1 mm-0.75 mm by the equation

CT₃(MPa)=57(MPa)−9.0(MPa)·ln(t)+49.3(MPa)·ln²(t)  (5).

Values of the nonlinear frangibility limits CT₁ and CT₃ for severalthicknesses in the range 0.3 mm to 1 mm (0.3 mm to 0.75 mm in the caseof CT₃) are summarized in Table 2. Thus, according to Barefoot I andBarefoot II, for thicknesses below 0.75 mm, glass in which CT_(A) isgreater than CT₃ poses an unacceptable risk (i.e., >5%) of beingfrangible. Similarly, for thicknesses above 0.75 mm, glass in whichCT_(A) is greater than CT₁ presents an unacceptable risk (>5%) of beingfrangible.

For thicknesses in the range 0.3 mm to 0.5 mm for the glass used byBarefoot I and Barefoot II, the onset of frangibility is observed whenthe DOL ranges between about 0.085t and 0.126t during ion exchange innominally pure KNO₃. As can be seen from FIG. 2, the ratio of CT_(A) tothe physical CT (labeled CT_(phys) in the equations below) ranges fromabout 1.373 to about 1.469 over that range of DOL/t, averaging about1.421. Hence, the ratio CT/CT_(A) ranges from about 0.681 to about0.728, with an average value of about 0.704. Therefore, the physical CTlimit corresponding to the prior-art CT_(A) limit for thicknesses0.3-0.5 mm (CT₃) is

CT_(phys)⁽³⁾(0.3mm≦t≦0.5mm)=(0.681÷0.728)×(57−9.0×ln(t)+49.3×(ln(t))²)  (6).

For thicknesses between about 0.5 mm and about 0.75 mm, the ratio DOL/tat which frangibility occurs in the examples is in the range0.064-0.085, where the ratio CT_(A)/CT_(phys) is about 1.332 to about1.374. Accordingly, the ratio CT_(phys)/CT_(A) ranges from about 0.728to about 0.751, and a frangibility limit in terms of physical centertension can be defined through its relation to the limit CT₃ of BarefootII as

CT_(phys)⁽³⁾(0.5mm≦t≦0.75mm)=(0.728÷0.751)×(57−9.0×ln(t)+49.3×(ln(t))²)  (7).

For samples having a thickness greater than 0.75 mm and not greater than1.0 mm, the relevant CT limit is CT₁, described in Barefoot I. The ratioof DOL/t at which frangibility occurs in the examples of Barefoot I istypically in the range 0.048 to 0.060, and the ratio CT_(A)/CT_(phys)ranges from about 1.302 to about 1.324, the inverse of which ranges from0.755 to 0.768.

Hence, for the thickness range 0.75 mm<t≦1.0 mm, the physical CTfrangibility limit can be derived from the Barefoot II empiricalfrangibility limit:

$\begin{matrix}{{{CT}_{phys}^{(1)}\left( {{0.75\mspace{14mu} {mm}} < t \leq {1.0\mspace{14mu} {mm}}} \right)} = {\left( {0.755 \div 0.768} \right) \times \left( {{{- 38.7}\left( \frac{MPa}{mm} \right) \times {\ln (t)}({mm})} + {48.2({MPa})}} \right)}} & (8)\end{matrix}$

TABLE 2 Frangibility CT limits, expressed in terms of CT_(A), forthicknesses between 0.3 mm and 1 mm, disclosed in Barefoot I andBarefoot II t (mm) 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 CT₁ 94.8 88.883.7 79.1 75 71.3 68 64.9 (MPa) CT₃ 139.3 120.8 106.6 95.6 86.9 80 74.570 (MPa) t (mm) 0.7 0.75 0.8 0.85 0.9 0.95 1 CT₁ 62 59.3 56.8 54.5 52.350.2 48.2 (MPa) CT₃ 66.5 63.7 (MPa)

As described herein, if the maximum CS in the glass and DOL aresubstantially different from those described by Barefoot I, the onset offrangibility may occur at substantially different CT_(A) value for theglass having the same overall composition and thickness. In an alkalialuminosilicate glass containing approximately 16 mol % Na₂O andessentially no K₂O, a 0.4-mm-thick substrate of the glass becomesfrangible when ion exchanged in a bath containing essentially pure KNO₃at 390° C. to a depth of layer of about 36 μm, as measured by a FSM-6000surface stress meter. The compressive stress produced by the samesurface stress meter during the measurement is about 920 MPa, and theCT_(A) is about 101 MPa. However, when ion exchanged at 440° C. for 11.7hours in a bath containing 37 wt % NaNO₃ and 63 wt % KNO₃ the glasshaving the same composition did not exhibit frangible behavior. Underthese ion exchange conditions, the glass developed a CS of 301 MPa, aDOL of 114.7 μm as measured by FSM-6000, and a CT_(A) of 202 MPa, whichis almost twice as great as the CT₃ frangibility limit for 0.4 mmthickness (106.6 MPa, Table 2). In another example, the same type ofglass was found frangible after ion exchange for 13.7 hours in the samebath and at the same temperature, with resulting compressive stress of279 MPa with depth of layer DOL of 120.6 μm and CT_(A)=212 MPa. Theseexperiments showed how the CT determined by the formula used in BarefootI can have a frangibility-limit value that is twice as large when theDOL is 30% of the thickness (0.3t), compared with the pure-bath casewhen the depth of layer was only 9% of the thickness.

In related experiments, a sample having a thickness of 0.50 mm exhibitednon-frangible behavior following ion exchange for 15.3 hours at 440° C.in the ion exchange bath containing 37% NaNO₃ and 63% KNO₃ by weight.The ion exchanged sample had CS of 304 MPa, DOL of 120.8 μm, and CT_(A)of 142 MPa, which is substantially higher than the Barefoot II CT₃ limitof 86.9 MPa for 0.5 mm thick glass (Table 2).

Furthermore, frangibility was not observed for samples that were ionexchanged for times exceeding 25 hours at 440° C. in a bath containing45 wt % NaNO₃ and 55% KNO₃. The DOL of these ion exchanged samplesexceeding 150 um. In one example, a 0.4 mm-thick sample acquired a CS of213 MPa, DOL of at least 149.3 μm, and CT_(A) of at least 314 MPafollowing ion exchange for 21 hours at 440° C. In another example, a 0.5mm-thick sample acquired a CS of 221 MPa, DOL of at least 147 μm, andCT_(A) of at least 172 MPa following ion exchange for 25.25 hours at440° C. Following ion exchange for 25.25 hours at 440° C., a samplehaving a thickness of 0.6 mm acquired a CS of 254 MPa, DOL of at least148 MPa, and CT_(A) of at least 124 MPa, which is substantially greaterthan CT₃ of 74.5 MPa observed for 0.6 mm thick glass. A substrate withthickness of 0.8 mm acquired a CS of 272 MPa, DOL of at least 144 μm,and CT_(A) of at least 76 MPa following ion exchange under the sameconditions. This is substantially greater than the CT₁ value of 56.8 MPaobserved for the same thickness and the CT₃ value of 59.3 MPa observedfor a thickness of 0.75 mm. A 1.0 mm thick substrate had a CS of 278MPa, which is substantially greater than the CT₁ value of 48.2 MPaobtained for the same thickness, a DOL of at least 142 μm, and a CT_(A)of at least 55 MPa.

Following ion exchange at 440° C. for times exceeding 30 hours in a bathcontaining 50 wt % NaNO₃ and 50 wt % KNO₃, frangibility was not observedfor 0.4 mm thick substrates, and depths of layer exceeding 170 um wereachieved. For ion exchange times of 14 hours and 20 minutes in the samebath, a compressive stress of 235 MPa, a DOL of at least 111 μm, and aCT_(A) of at least 150 MPa were obtained. Following ion exchange for16.7 hours at 440° C. in the 50 wt % NaNO₃/50 wt % KNO3 bath, acompressive stress of 227 MPa and DOL of at least 131 μm were measured,with CT_(A) of at least 215 MPa. For ion exchange times of 17.7 to 20.7hours, 25 hours, and 30 hours, the FSM-6000 was not able to estimate DOLand CT_(A), but DOL would have been greater than 131 μm and CT_(A) wouldhave been greater than about 215 MPa.

Due to very limited ability to measure DOL beyond 100 μm DOL, andespecially beyond about 130 μm DOL, the FSM-6000 instrument was unableto estimate the depth of layer and CT_(A) for the deepest profiles. TheFSM-6000 usually underestimates DOL when DOL is greater than about 100μm—and especially when the DOL is greater than 130 μm—due to the limitedability of the instrument to resolve the dark lines of the modespectrum, which become very dense when the DOL is very large.

In a related experiment, samples of the same glass with greaterthicknesses of 0.5, 0.6, 0.8, and 1.0 mm were each ion exchanged for 26hours and 43 hours at 440° C. in a bath containing 50 wt % NaNO₃ and 50wt % KNO₃. All of the ion exchanged samples were non-frangible. Becausethe depths of layer of these samples exceeded 150 μm, the DOL and CT_(A)could not be measured using the FSM-6000 instrument.

In the above examples, the DOL measured using the FSM-6000 instrumentexceeded 0.1t, and the CT_(A) value at which frangibility was firstobserved was significantly higher than the CT₁ frangibility valuesdetermined by the empirical equations of Barefoot I and Barefoot II.

As demonstrated by the above examples, when DOL>0.1t, as the allowablephysical CT exceeds the CT₁ and CT₃ frangibility limits previouslyprescribed and a combination of relatively high CS and large DOL can beused to obtain stronger glass.

The actual physical central tension inside the mid-plane of the sampleusually differs from the approximate value CT_(A), which has been widelyadopted due to its ease of calculation based on the known thickness andthe CS and DOL that are usually reported by the FSM-6000. Assuming thatthe associated index profile is a linear truncated profile, the FSM-6000estimates DOL from the measured number of guided optical modes in theion-exchanged layer. In practice, however, the index profile differsfrom a linear truncated profile, especially at the deeper end of theprofile.

In many cases, the profile may be closely approximated by acomplementary error function (erfc). This is usually the case when theeffective diffusion coefficient of the ion exchange (mutual diffusioncoefficient) varies relatively little over the concentration rangespanned by the concentration profile of the diffusant. Such is the casefor the K⁺ for Na⁺ exchange in the glass described by Barefoot I andBarefoot II, which disclosed the CT₁ and CT₃ frangibility limitsobserved in those glasses. The central tension CT for an erfc-shapeddistribution of the K⁺ concentration can be calculated by taking intoaccount that the local change in specific volume is proportional to thelocal K⁺ concentration and by applying the requirement of force balance,which requires that the spatial integral of the stress in thecompression regions of the substrate be equal and opposite in sign tothe integral of the stress over the tension region.

The ratio of the approximate adopted CT_(A) and the calculated truephysical CT (CT(erfc)) for the erfc profile characteristic of lineardiffusion is shown in FIG. 2 as a function of the ratio of the depth oflayer DOL, where DOL is calculated by the FSM-6000 for the sameerfc-shaped index profile, with the FSM-6000 considering it as a lineartruncated profile to the thickness of the layer.

If the concentration profile of the chemically strengthening ion followsthe functional form in the linear-diffusion case:

$\begin{matrix}{{{C(x)} = {C_{0}{{erfc}\left( \frac{x}{x_{0}} \right)}}},} & (9)\end{matrix}$

where x₀ is an effective penetration depth, it relates to theFSM-measured DOL by the equation

DOL=1.3825x ₀  (10).

The CT is then determined from CS from force balance:

$\begin{matrix}{{\int_{0}^{DOC}{\sigma \ {x}}} = {\int_{DOC}^{\frac{t}{2}}{\sigma \ {{x}.}}}} & (11)\end{matrix}$

The ratio of the physical CT to the CS then depends on the DOL in thefollowing way:

$\begin{matrix}{\frac{CT}{CS} = {\frac{\frac{2\; {DOL}}{1.3825\; t\sqrt{\pi}}\left( {1 - ^{- \frac{1.3825^{2}t^{2}}{4\; {DOL}^{2}}}} \right)}{{\frac{2\; {DOL}}{1.3825\; t\sqrt{\pi}}\left( {1 - ^{- \frac{1.3825^{2}t^{2}}{4\; {DOL}^{2}}}} \right)} + {{erfc}\left( \frac{1.3825\; t}{2\; {DOL}} \right)} - 1}.}} & (12)\end{matrix}$

On the other hand, the FSM formula for CT_(A) is

$\begin{matrix}{{{CT}_{A} = \frac{{CS} \times {DOL}}{t - {2\; {DOL}}}},} & (13)\end{matrix}$

and the ratio of the traditionally adopted approximate CT_(A) to thephysical CT for the linear-diffusion case (erfc-profile) is Therefore:

$\begin{matrix}{\frac{{CT}_{A}}{CT} - {\frac{1}{1 - \frac{2\; {DOL}}{t}}{\frac{{\frac{DOL}{0.69\; t\sqrt{\pi}}\left( {1 - ^{- \frac{0.478t^{2}}{{DOL}^{2}}}} \right)} + {{erfc}\left( \frac{0.69\; t}{DOL} \right)} - 1}{0.816\left( {1 - ^{- \frac{0.478t^{2}}{{DOL}^{2}}}} \right)}.}}} & (14)\end{matrix}$

Frangibility limit CT₁ in terms of CT_(A), and the correspondingphysical CT limit are calculated from CT₁ assuming the DOL is 0.03,0.04, and 0.05 mm as commonly measured by the surface stress meterFSM-6000. For the range of thicknesses>0.3 mm, and ion exchange for theglass composition described in US Barefoot I in nominally pure KNO₃, theCS is between about 700 and 900 MPa, and the DOL is greater than about0.03 mm at the onset of frangibility. In terms of CT_(A) the regionabove the CT₁ curve is frangible according to the prior art. This meansthat in terms of physical CT the entire region above the continuous linerepresenting CT_(erfc) for DOL=0.03 mm, is considered frangibleaccording to the prior art.

The boundary separating the regions of frangible and non-frangible glassin the two-dimensional space of thickness and CT are shown in FIG. 3.FIG. 3 includes the separating line defined in terms of CT_(A) accordingto Barefoot II ((a) in FIG. 3) and three other lines expressed in termsof physical CT and calculated for erfc-shaped profiles having the sameCT_(A) as Barefoot I are shown. These lines were calculated fordifferent DOLs measured using the FSM-6000 stress meter and representthe range of typical DOLs for which frangibility occurs in the glassdisclosed by Barefoot II following ion exchange in nominally pure KNO₃.Of these, the highest CT limit representing the CT_(A) curve in terms ofphysical CT is the one corresponding to the smallest DOL (0.03 mm; lineb in FIG. 3).

For thicknesses greater than 0.75 mm, the space above the curvesrepresents conditions for frangible glass in terms of CT_(A) or physicalCT, depending on the curve.

The boundary separating the regions of frangible and non-frangible glassin the two-dimensional space of thickness and CT after ion exchange innominally pure KNO₃, based on the criterion expressed by CT₃, is shownin FIG. 4. FIG. 4 includes the separating line defined in terms ofCT_(A) ((a) in FIG. 3) as well as three other erfc-shaped profilesexpressed in terms of physical CT. These profiles have the same CT_(A)as the line a, and were calculated for different DOLs as measured byFSM-6000. These profiles represent the range of typical DOLs for whichfrangibility occurs in the glass disclosed in Barefoot II. Of the linesshown in FIG. 4, the highest physical CT limit representing the CT_(A)curve in terms of physical CT is the one corresponding to the smallestDOL.

Since frangibility for pure KNO₃ ion exchange bath and thickness t>0.3mm occurs generally at DOL>0.03 mm, the entire region above the curve inFIG. 4 corresponding to DOL=0.03 mm (curve b) is a region offrangibility according to Barefoot I.

The particular glass composition used for demonstrating the embodimentsof the present disclosure is described in U.S. patent application Ser.No. 13/678,013 by Timothy M. Gross, entitled “Ion Exchangeable Glasswith High Crack Initiation Threshold,” filed Nov. 15, 2012, and U.S.Pat. No. 8,765,262 by Timothy M. Gross, entitled “Ion Exchangeable Glasswith High Crack Initiation Threshold,” filed Nov. 15, 2012, bothclaiming priority to U.S. Provisional Patent Application No. 61/560,434filed Nov. 16, 2011. This glass contained Na₂O as the dominant alkalioxide with a negligible amount of K₂O in the base substrate, as a resultof imperfect elimination of K₂O from the starting raw materials. In thiscase, substantially nonlinear diffusion occurs during the ion exchangeof K⁺ for Na⁺, where the mutual diffusion coefficient is low in regionswith low K⁺ concentrations, and is substantially higher in those regionswhere the K⁺ concentration is a large fraction (>25%) of the totalconcentration of K⁺ and Na⁺. In such instances, the shape of the error(erfc) function does not accurately represent the shape of the index andstress profiles, and a detailed nonlinear diffusion model is necessaryto accurately describe the profiles and their relationship toion-exchange conditions. Detailed stress profile extraction using anIWKB-based algorithm described in Roussev I (U.S. patent applicationSer. No. 13/463,322, previously cited hereinabove. Examples of non-erfcextracted index profiles of an actual substrate are shown FIG. 5, whichis a plot of transverse magnetic (TM) and transverse electric (TE) indexprofiles extracted by the IWKB-based algorithm up to the turning pointof the last captured optical mode via prism coupling measurements. Theglass substrate was a 0.4-mm-thick glass that was ion exchanged 17.7hours at 440° C. in a bath containing 50% NaNO₃ and 50% KNO₃ by weight.The glass substrate composition is described in U.S. patent applicationSer. No. 13/678,013. The shapes of the index profiles differsubstantially from the erfc-shape. FIG. 6 is a plot of a stress profilefor a 0.4 mm-thick glass that was exchanged 17.7 hours at 440° C. in abath containing 50% NaNO₃ and 50% KNO₃ by weight. The composition of theglass sample is described in U.S. patent application Ser. No.13/678,013. The stress profile has a compressive stress at the surface(depth=0 μm) of 219 MPa, a depth of compression DOC of 78 μm, and acentral tension CT of 86 MPa. This physical CT is substantially higherthan the physical CT limit of 62 MPa, as taught by Barefoot I, for aglass having a thickness of 0.4 mm. The difference CT−CS is about 86MPa−(−219 MPa)=305 MPa.

The elastic energy per unit area, integrated along the depth dimension,is estimated to be about 13.4 J/m² in the compression region, and about15.7 J/m² in the tension region. Hence, the total elastic energy isapproximately 29.1 J/m². Considering the thickness of 0.4 mm, the totalelastic energy per unit thickness is 72.8 J/(m²·mm).

By applying the condition of force balance between the depth integral ofthe stress over the compression region and the depth integral of thestress over the tension region, the value of the actual physical centraltension CT can accurately be determined. This physical CT shouldgenerally correspond to the erfc-based physical CT that may becalculated in the essentially linear-diffusion case previouslymentioned. The stress profile found by the IWKB method is usuallylimited to the depth of the smaller of the deepest turning points forthe TM and TE optical modes of the waveguide region. When the DOL isvery large, the stress profile at depths approaching these largestdepths is sometimes subject to significant noise. Hence, a parabolicapproximation for the shape of the stress profile between the depth ofcompression DOC is employed, and the larger depth at which the profilebecomes essentially flat at the depth of chemical penetration, havingstress substantially equal to the central tension from that depth to thecenter of the substrate. An example of the stress profile extractedusing the IWKB method is shown in FIG. 7. The solid line (line a) inFIG. 7 represents the quadratic approximation adopted to emulate theprofile shape in the tension zone for accurate estimate of the stressintegral in the tension zone. The variable part of the stress profile inthe tension zone is represented by a parabola (dashed line (b) in FIG.7) extending between the depth of compression (DOC) and the depth equalto 1.15·DOL. For the particular glass described hereinabove, the depthof profile flattening is approximately 1.15·DOL, where DOL is determinedby the FSM-6000 instrument for the same ion exchanged glass. In thosecases where the stress profile could be extracted with very low noise,the deepest portion of the stress profile has a stress that approachesthe central tension found by the above method of force balance betweentension and compression forces. The force balance condition representsthe fact that, in the absence of external forces, the sample shaperemains unchanged in time.

For the particular example shown in FIGS. 4 and 5, the difference CT−CSis about 305 MPa where, according to accepted physics conventions,tensile stress is positive and compressive stress negative. Frangibilitydid not occurred during the ion exchange of glass having a thickness of0.4 mm in a bath containing 50 wt % NaNO₃ and 50 wt % KNO₃, even whenion exchange times exceeded 30 hours and the stress profiles (at a levelwhere the signal of the stress measurement is approximately equal to thenoise level) from the two sides of the substrate closely approached thecenter of the sample.

In the absence of stress relaxation during and post ion exchange, theconcentration difference CT−CS=|CT|+|CS| between the maximumconcentration of the diffusant (K⁺) and its minimum concentration in thecenter, is directly associated with the composition of the ion exchangebath and the ion exchange temperature. This difference remains largelyindependent of ion exchange time, until eventually the profiles from thetwo ends of the substrate meet in the middle and a measurable increaseof the diffusant (K⁺, or K₂O) concentration occurs in the center. Atthat point the concentration difference between the maximumconcentration and the minimum concentration is reduced, and thedifference CT−CS thus starts to decrease beyond that point even in theabsence of stress relaxation. At temperatures below 450° C. and ionexchange salt mixture compositions in which NaNO₃ comprises at least 30wt % in the NaNO₃+KNO₃ ion exchange bath, stress relaxation isrelatively small. In addition, the difference CT−CS decreases veryslowly with increasing ion exchange time and FSM DOL (due to the smallstress relaxation) and may therefore be approximated as being constant.Hence, it has been found that for CT−CS≦305 MPa, the ion exchangedsubstrate does not become frangible even if the physical CTsubstantially surpasses any CT corresponding to previously disclosed CTlimits, and the substrate may in fact never become frangible as long asthe above inequality is observed. This case is valid for all substratethicknesses greater or equal to the 0.4 mm thickness described herein.

In addition, no frangibility was observed for substrates that were ionexchanged for up to about 42 hours at 440° C. in a mixture containing 45wt % NaNO₃ and 55 wt % KNO₃ and having CT−CS differences, depending onsample thickness, ranging approximately from about 311 MPa to about 324MPa.

In one aspect, strengthened glass having a physical CT above thepreviously known frangibility CT limit (curve a in FIG. 3), DOL>0.1t,and CT−CS of less than or equal to about 350 MPa and, in someembodiments, less than or equal to about 340 MPa, does not exhibitfrangible behavior regardless of the depth of layer. Accounting formoderate amounts of stress relaxation, the CT−CS difference at short ionexchange times (i.e., 10 μm≦DOL_(short)≦40 μm). When applying theconvention normally used in the art (i.e., compression is expressed as anegative (<0) stress and tension is expressed as a positive (>0)stress), the CT−CS difference may be alternatively expressed as|CT|+|CS|≦350 MPa.

In another aspect, a regime where the onset of frangibility may belimited not by achieving a CT required to propagate a flaw quicklythrough the tensile central region of the glass can be obtained, butrather by the amount of stored elastic energy when the DOL is large,generally DOL>0.1t. In particular, conditions could be obtained wherethe CT may exceed the previously disclosed frangibility CT limit whenthe DOL is greater than about 0.15t. If the amount of stored elasticenergy in the compression and tension regions is not adequate for theformation of large, new, free surfaces during crack propagation andbifurcation, then frangibility is prevented.

The elastic energy stored by the stress profile is calculated accordingto the equation

$\begin{matrix}{{W_{el} = {\frac{\left( {1 - v} \right)}{E}{\int{\sigma^{2}{x}}}}},} & (15)\end{matrix}$

where ν is the Poisson ratio (0.22 for the exemplary glass compositiondescribed hereinabove), E is Young's modulus (about 68 GPa for ourexample glass 5318), and σ is the stress.

The elastic energy per unit area of glass in each compression region(one on each major outer surface of the substrate) is:

$\begin{matrix}{W_{el}^{comp} = {\frac{1 - v}{E}{\int_{0}^{DOC}{\sigma^{2}\ {{x}.}}}}} & (16)\end{matrix}$

The elastic energy in the tension region from the compression depth tothe center of the glass substrate is:

$\begin{matrix}{W_{el}^{tens} = {\frac{1 - v}{E}{\int_{DOC}^{0.5\; t}{\sigma^{2}\ {{x_{W}}.}}}}} & (17)\end{matrix}$

The total elastic energy stored in the substrate is twice the sum of theelastic energy of a single compression and the tension region,multiplied by 2 to account for two compression regions region and onehalf of the central tension region occurring in a chemicallystrengthened substrate. The units for the different variables in theabove equations are as follow:

for stress: [α]=MPa≡10⁶N/m²  (18);

for depth: [x]=μm=10⁻⁶m  (19);

-   -   for elastic energy per unit substrate area:

$\begin{matrix}{{\left\lbrack W_{el} \right\rbrack = {{{MPa}^{- 1}*{MPa}*10^{6}\frac{N}{m^{2}}*10^{- 6}m} \equiv \frac{N*m}{m^{2}} \equiv \frac{I}{m^{2}} \equiv \frac{µJ}{{mm}^{2}}}};} & (20)\end{matrix}$

and for elastic energy per unit substrate area per unit thickness:J/m²·mm.

Using the quadratic approximation for the variable portion of the stressin the tension region, with a chemical depth d_(chem)=1.15·DOL_(FSM),application of the force-balance condition results in the followingspecific equation for determining the physical CT for the particularglass composition and profiles considered:

F=∫ ₀ ^(DOC)σ(x)dx  (21),

which is found by integrating the stress over the compression region ofthe profile as extracted by the IWKB-based algorithm

$\begin{matrix}{{CT} = {\frac{F}{{0.5\; t} - {\frac{2}{3}{DOC}} - {\frac{1}{3}d_{chem}}}.}} & (22)\end{matrix}$

The energy in the compression region is found directly by integratingthe square of the stress, through the definition equation for energy inthe compression region (equation 7) previously described. The expressionfor the energy in the tension region that is valid in the specific casewith the quadratic approximation for the variable portion of the profilein the tension zone is:

$\begin{matrix}{W_{cl}^{tens} = {\frac{1 - v}{E}{{{CT}^{2}\left( {{0.5\; t} - d_{chem} + {\frac{8}{15}\left( {d_{chem} - {DOC}} \right)}} \right)}.}}} & (23)\end{matrix}$

Results obtained for glasses having thicknesses ranging from 0.4 mm to1.0 mm are summarized in Tables 3 and 3a. Table 3 lists the compressivestress CS determined by the IWKB method, depth of layer DOL estimatedfrom the TM and TE spectra obtained using the FSM6000 stress meter, thethickness, the depth of compression, and the physical center tension CT.Table 3a lists the compressive energy (“Compr” in Table 3a), tensileenergy, total energy, CT_(A) and CT−CS values, and results offrangibility testing. The glasses listed in Tables 3 and 3a were ionexchanged at 440° C. for various times in a bath containing about 45 wt% NaNO₃ and about 55 wt % KNO₃. In these examples the DOL determined bythe FSM-6000 ranges from about 0.14t to about 0.39t. As previouslymentioned, the CT−CS difference ranges from about 311 MPa to at least324 MPa. Depending on the thickness and DOL, the CS ranges from about222 MPa to about 270 MPa. All glass samples listed in Table 3 were foundto be non-frangible. For all thicknesses, the physical CT exceeded thephysical CT frangibility limit corresponding to prior art limits, andCT_(A) exceeded the prior-art CT_(A) limit.

TABLE 3 Examples of non-frangible ion exchanged glass with DOL > 0.1t.DOL DOL FSM FSM CT CS TM TE DOC phys. IWKB (est.) (est.) t mm μm MPa 21−221.6 151.1 157.8 0.4 81.6 102.7 25.25 −236.4 153.7 149.7 0.5 91.6 79.625.25 −247.5 151.5 155.6 0.6 98.6 65.6 25.25 −268.1 153.1 152.5 0.8107.2 49.0 30 −261.7 169.9 170.1 0.8 116.2 53.7 36 −254.5 172.9 164.60.8 120.6 56.1 42 −250.4 185.5 185.8 0.8 127.6 60.8 25.25 −285.2 142.7148.8 1.0 114.8 39.3 30 −270.2 165.0 162.2 1.0 124.0 42.5 36 −270.2166.1 172.1 1.0 128.0 44.9 42 −264.3 182.1 182.3 1.0 135.8 48.4

TABLE 3a Examples of non-frangible ion exchanged glass with DOL > 0.1t.Compr Tension Total Total Energy Energy Energy Energy/t Frangi- [J/m²][J/m²] [J/m²] [J/m² mm] CT_(A) CT-CS bility 21 15.1 8.9 48.0 120.0 375.0324.3 NF 25.25 18.7 8.7 54.8 109.7 183.1 316.0 NF 25.25 21.5 8.1 59.498.9 130.3 313.0 NF 25.25 26.7 7.2 67.7 84.6 83.5 317.1 NF 30 26.6 8.269.6 86.9 96.2 315.4 NF 36 27.1 8.9 71.9 89.9 93.3 310.6 NF 42 27.5 9.874.7 93.4 108.7 311.2 NF 25.25 30.3 6.4 73.4 73.4 58.6 324.5 NF 30 30.27.2 74.7 74.7 66.4 312.7 NF 36 31.4 7.9 78.6 78.6 69.7 315.1 NF 42 32.08.8 81.7 81.7 76.2 312.7 NF

Following ion exchange at 440° C. for 21 hours in a bath containingabout 45 wt % NaNO₃ and about 55 wt % KNO₃ the sample having a thicknessof 0.4 mm exhibited a depth of compression DOC of 81.6 μm, physical CTof at least 102.7 MPa, stored elastic energy in the compression regionof 15.1 J/m², and stored elastic energy in half of the tension region ofat least 8.9 J/m². The total elastic energy is at least 48 J/m² which,when normalized to thickness, is at least 120 J/m²·mm. In thisembodiment, a new non-frangible region where the DOL is greater thanabout 0.1 t has been found for the thickness of 0.4 mm. The physical CTis greater than the approximately 63 MPa value consistent with previousdisclosures. The physical CT is greater than the 76 MPa value, which isconsistent with CT_(A)=CT₃=106.6 MPa for 0.4 mm sample thicknesses ofBarefoot I and Barefoot II.

In another example, a 0.4 mm thick sample ion exchanged for 26.5 hoursat 440° C. in a bath comprising about 50 wt % NaNO₃ and 50 wt % KNO₃ hada CS of about 191 MPa, a CT of at least 94 MPa, and a DOC of about 85 μmand was found to be non-frangible. The physical CT was substantiallyhigher than the physical value of 76 MPa, which corresponds to thepreviously disclosed value CT_(A)=CT₃=106.6 MPa for the same thickness.

Tables 4 and 4a list examples of non-frangible and frangible ionexchanged glass samples with DOL>0.1t and having thicknesses rangingfrom 0.4 mm to 0.8 mm. Each of the samples was ion exchanged at 440° C.in a bath containing about 40 wt % NaNO₃ and 60 wt % KNO₃. Table 4 liststhe ion exchange time, compressive stress CS determined by the IWKBmethod, depth of layer DOL estimated from the TM and TE spectra obtainedusing the FSM6000 stress meter, sample thickness, the depth ofcompression, and the physical center tension CT. Table 4a lists the ionexchange time, compressive energy (“Compr” in Table 4a), tensile energy,total energy, CT_(A) and CT−CS values, and results of frangibilitytesting (“F” denotes frangible behavior, and “NF” denotes non-frangiblebehavior). Samples that were ion exchanged for 42.6 hours have aFSM-style depth of layer DOL substantially greater than 150 μm, and someof the high-order modes may not have been detected due to difficultyresolving these densely spaced modes. Hence, the calculated values ofDOL, physical CT, tension energy, and total elastic energy representlower-limit estimates of actual values. Non-frangible examples exhibitCT−CS values of up to 334 MPa. In the three non-frangible examples, thephysical CT substantially exceeds previously reported corresponding CTlimits for the thicknesses of 0.6 mm (CT<52 MPa), 0.8 mm (CT<44.3 MPa),and 1.0 mm (CT<38 MPa). Respectively.

TABLE 4 Examples of non-frangible and frangible glass with DOL > 0.1tand various thicknesses, after ion exchange in a bath containing about40 wt % NaNO₃ and 60 wt % KNO₃ at 440° C. DOL DOL Ion (μm) (μm) exchangeCS FSM FSM CT time (MPa) TM TE DOC phis (hours) IWKB est. est. t [mm](MPa) (MPa) 21.5 −227.9 154.8 158.3 0.4 84.6 115.5 25.7 −255.0 146.7153.4 0.6 100.2 70.2 25.5 −281.4 143.5 150.0 0.8 109.0 52.5 42.6 −272.2185.0 183.9 1.0 139.0 52.8

TABLE 4a Ion exchange times, compressive energy, tensile energy, totalenergy, CT_(A) and CT- CS values, and results of frangibility testingfor the samples listed in Table 4. IX time at 440 C. in 40 Compr TensionTotal Total wt % NaNO₃ Energy Energy Energy Energy/t CT_(A) CT-CSFrangi- 60 wt % KNO₃ [J/m²] [J/m²] [J/m²] [J/m² mm] (MPa) (MPa) bility21.5 17.2 10.9 56.2 140.4 415.9 343.4 F 25.7 24.2 9.4 67.3 112.1 129.8325.2 NF 25.5 30.2 8.3 77.1 96.4 82.2 333.9 NF 42.6 36.9 10.4 94.6 94.680.2 325.0 NF

In another example, listed in Tables 4 and 4a, a 0.4 mm thick glasssample ion exchanged for 21.5 hours was found to be frangible, having atotal stored elastic energy of about 56.2 J/m² which, when normalized tothickness, equaled about 140.4 J/m² mm. Hence, the newly discoverednon-frangible region described herein is characterized as having storedelastic energy of less than 56.2 J/mm² for a 0.4 mm glass samplethickness, and the elastic energy normalized to thickness is less than140.4 J/m² mm for all thicknesses, particularly for thicknesses greaterthan or equal to 0.4 mm.

In another example, listed in Tables 3 and 3a, a 0.5 mm thick glasssample ion exchanged for 25.25 hours was found to be non-frangible glasswith CT of 9.6 MPa. This CT is significantly greater than the value ofabout 56 MPa reported by Barefoot I for a 0.5 mm sample thickness and0.04 mm DOL. The CT_(A) of this sample listed was estimated to be 183MPa, which is much greater than CT₃ (0.5 mm) of 86.9 MPa. The DOC of thesample was as high as 91.6 μm, the energy in the compression region was18.7 J/m², and the energy in the tension half-region was at least 8.7J/m². The total stored elastic energy was at least 54.8 J/m² which, whennormalized to the thickness, was at least 109.7 J/m²·mm. The CT−CSdifference was about 316 MPa.

A 0.6 mm thick sample listed in Tables 3 and 3a was ion exchanged at for25.25 hours and found to be non-frangible. The ion exchanged sample hada CS of about 248 MPa, a DOL of about 153 μm, a DOC of 98.6 μm, and aphysical CT of at least 65.6 MPa, the latter being substantially abovethe limit of about 51 MPa reported by Barefoot I in terms of physical CTfor DOL of about 40 μm. The CT_(A) was estimated to be 130 MPa, which issubstantially greater than the previously reported CT₃ of 75.5 MPa. Theestimated elastic energy in the compression region was 21.5 J/m², and inthe tension region it was approximately 8.1 J/m². The total elasticenergy was about 59.4 J/m², and elastic energy per unit area and unitthickness was about 98.9 J/m² mm.

A 0.6 mm thick sample listed in Tables 4 and 4a was ion exchanged for25.7 hours and found to be non-frangible. The ion exchanged sample had aCS of about 255 MPa, a DOL of about 150 μm, a DOC of 100 μm, and evenhigher physical CT of about 70.2 MPa, which was substantially higherthan the previously reported value of about 56 MPa. Similarly, thenon-frangible sample exhibited CT_(A) of 129.8 MPa, which issubstantially greater than the previously reported frangibility limitCT_(A)=CT₃(0.6 mm)=74.5 MPa. The elastic energy in the compressionregion was about 24.2 J/m², and at least 39.4 J/m² in the tensionhalf-region. The total elastic energy was estimated to be at least 67.3J/m², and the elastic energy per unit area and unit thickness was atleast 112 J/m² mm.

A sample having a thickness of 0.8 mm (Tables 3 and 3a) was ionexchanged for 25.25 hours and found to be non-frangible with CS of about268 MPa, a DOL of about 153 microns, a DOC of about 107 μm, a andphysical CT of about 49 MPa. The physical CT is higher than the 43.5 MPafrangibility limit in terms of physical CT corresponding tocorresponding to CT_(A)=CT₁ for a thickness of 0.8 mm. The elasticenergy in the compression region was 26.7 J/m², while the tensionhalf-region had an elastic energy of 7.2 J/m² in. The total elasticenergy was about 67.7 J/m² which, when normalized to thickness, is about84.6 J/m² mm.

Another sample having a thickness of 0.8 mm and listed in Tables 4 and4a exhibited non-frangible behavior following ion exchange for 25.5hours. The sample had a CS of about 281 MPa, a DOL of about 146 μm, aDOC of about 109 μm, and a physical CT of about 45 MPa, the latter beingsubstantially greater than the prior-art limit in terms of physical CT(43.5 MPa) for a thickness of 0.8 mm. The elastic energy was about 30.2J/m² in the compression region, and about 10.6 J/m² in the tensionhalf-region, resulting in a total of about 77.1 J/m². The elastic energydensity, i.e., the elastic energy per unit area and unit thickness, wasabout 96.4 J/m² mm. The difference CT−CS of this non-frangible glass wasat least about 334 MPa.

Four examples of deep ion exchange of 1 mm thick glass substrates arelisted in Tables 3 and 3a. Ion exchange was carried out at 440° C. onthese samples for 25.25, 30, 36, and 42 hours. The resulting physical CTvalues were estimated to be 39.3 MPa, 42.5 MPa, at least 44.9 MPa, and48.4 MPa, respectively. The values may be underestimated, particularlyfor the 36 hour ion exchange, due to the DOL exceeding 160 μm, whichpresents challenges for precise resolution of the high-order modes. TheCT_(A) values ranged from about 58.6 to about 76.2 MPa, and were allsubstantially above the prior-art limit CT₁=48.2 MPa. The DOL rangedfrom about 143 μm to over 170 μm, while the DOC ranged from about 115 μmto about 136 μm. The difference CT−CS ranged from about 313 MPa to about325 MPa. The total stored elastic energy ranged from about 73.4 81.7J/m² to at least about 81.7 J/m² and the average energy density was 81.7J/(m²·mm).

A sample having a thickness of 1.0 mm, listed in Tables 4 and 4a, wasion exchanged for 42.6 hours. The resulting strengthened glass wasnon-frangible, with CS of about 272 MPa, and a physical CT of at leastabout 52.8 MPa, which was substantially above the physical CTfrangibility limit estimate of 37 MPa for 1 mm thick glass with DOL ofabout 50 μm. The CT_(A) of the non-frangible samples was about 80.2 MPa,which is substantially higher than the Barefoot I frangibility limit ofCT_(A)=CT₁(1 mm)=48.2 MPa. The DOL was estimated to be about 185 μm orgreater, the DOC was about 139 μm, and the elastic energy was about 36.6J/m² in the compression region and greater than about 10.4 J/m² in thetension half-region. The total elastic energy was at least 49.9 J/m²,and represents an average elastic energy density of at least 49.9 J/m²mm.

The examples summarized above demonstrate that, when the DOL accountsfor an appreciable fraction of the glass thickness, the CT value atwhich frangibility occurs can vary with DOL, depending on the storedtotal elastic energy. The total elastic energy becomes even moresignificant in the case of double-ion-exchanged glass having a deepregion of moderate compression and a shallow region of high compressionin which the stress varies strongly with depth (FIGS. 7 and 8). Thesample represented in FIGS. 7 and 8 was double-ion exchanged 0.55 mmthick glass. The first ion exchange step included ion exchange at 450°C. for 7.75 hours in a 40 wt % NaNO₃/60 wt % KNO₃ molten mixture. Thefirst ion exchange step produced the deep, slowly-changing portion A ofthe stress profile. In the second step, the glass was ion exchanged at390° C. for 12 minutes in a bath containing approximately 99.5 wt % KNO₃and 0.5 wt % NaNO₃, and produced the shallow steep region B of thestress profile. Samples with this stress profile are unlikely to befrangible, although any significant even minor additional ion exchangeto increase the depth of the first or second region would result in afrangible glass. The IWKB analysis revealed a CS of about 891 MPa, a DOCof about 70.6 microns, and a physical CT of about 61 MPa, which issimilar to the frangibility limit of physical CT limit corresponding toCT_(A)=CT₃(0.55 mm) The elastic energy was about 44.7 J/m² in thecompression region, and about 7.8 MJ/m² in the tension half-region. Thetotal elastic energy was about 105 J/m2, representing an average energydensity of about 191 J/m² mm. This is the highest average elastic energydensity that has been observed in non-frangible samples having a largechemical penetration depth of greater than about 0.12t, and CTAsubstantially above the CT₃ prior-art frangibility limit.

As described herein, when the DOL accounts for an appreciable (i.e.,10%) fraction of the glass thickness, the value of CT at whichfrangibility occurs may vary with DOL, depending on the stored totalelastic energy. The total elastic energy plays an even greater role inwhen the glass is strengthened by a two-step—or double—ion exchangeprocess, in which the glass is provided with a deep region of moderatecompression, and a shallow surface region of high compression where thestress varies with depth very quickly (FIG. 8). FIG. 8 is a plot of thestress profile for double-ion exchanged 0.55 mm-thick glass. The firststep involved ion exchange for 7.75 hours at 450° C. in a molten mixtureof 40 wt % NaNO₃ and 60 wt % KNO₃. The first step produced the deepslowly-changing portion (A) of the stress profile. In the second step,the glass was ion exchanged at 390° C. for 12 minutes in a bathcontaining approximately 99.5 wt % KNO₃ and 0.5 wt % NaNO₃, producingthe shallow steep region (B) of the stress profile

Samples having the stress profile shown in FIG. 8 were found to benon-frangible, although any significant additional ion exchange toincrease the depth of the first or second region would result infrangible glass. The IWKB analysis of the glass revealed a CS of about891 MPa, a DOC of about 70.6 μm, and a physical CT of about 61 MPa, thelatter being substantially above the frangibility limit in terms ofphysical CT estimated based on previous guidelines for strengthenedglasses having a thickness of 0.55 mm and a DOL of 40 μm.

The elastic energy of the sample shown in FIG. 6 was about 44.7 J/m² inthe compression region, and about 9.5 MJ/m² in the region under tension.The total elastic energy was about 54.1 J/m², representing an averageenergy density of about 98.4 J/m²·mm. This is the highest averageelastic energy density that has been observed in non-frangible samples.It is estimated that the maximum average elastic energy density fornon-frangible glass over the thickness range from 0.4 mm to 1 mm liesbetween about 98 J/m² mm and 116.5 J/m² mm, the latter value being thelowest value where 0.4 mm-thick glass with large DOL was observed to befrangible.

In some embodiments, the elastic energy density is less than about 200J/m²·mm. In other embodiments, the elastic energy density is less thanabout 140 J/m²·mm and, in still other embodiments, the elastic energy isless than about 120 J/m²·mm.

FIG. 9 represents the TE and TM refractive index profiles for the samplewhose stress profile is shown in FIG. 8. For the ion exchange of K⁺ forNa⁺, the refractive index increases as a result of the ion exchange, andthe index profile is a monotonic function of depth, making it convenientto use IWKB analysis for the extraction and evaluation of stressprofiles. The index profiles of FIG. 9 show that, other thanapproximating the surface compressive stress the DOL, the FSM-6000 willsignificantly under-estimate the chemical penetration depth for the deepregion and will not provide direct information about the steep shallowregion in the case of double-ion-exchange (DIOX) profiles. This isbecause the widely used DOL reported by FSM-6000 is calculated assumingthat the index profile is well represented by a single linear segmenthaving a single fixed slope and a single depth of penetration. Thewidely used CT_(A) calculated based on the DOL obtained using theFSM-6000 and the surface CS is often 2 to 3 times greater than thephysical CT for the DIOX profile, and is therefore not convenient to useas a predictor of frangibility. It should be clear that the analysisrevealed in the present disclosure in terms of physical CT and storedelastic energy has a much broader realm of application than theCT_(A)-based criteria.

In addition, stress profiles having large compression depth in somecases can be obtained using ion exchange that does not lead to anincrease of the refractive index, such as, for example, during theexchange of Na⁺ for Li⁺ in a glass substrate that is rich in Li₂O. Whilethe traditionally used DOL based on measurement of the number of guidedoptical modes is not available in these cases, the compression depth DOCis still a physical quantity that can be measured by various polarimetrytechniques and represent the depth of chemical strengthening. As can beseen in Tables 1 and 2 below, the DOC is greater than 0.1t, usuallyexceeds 0.12t, and most often exceeds 0.15t for all examples ofnon-frangible glass with physical CT exceeding the prior-artfrangibility limit.

The criterion for non-frangibility that is based on the difference CT−CSregardless of DOL can be equivalently restated as the non-frangibilityregion for CT−CS<330 MPa when using a salt composition and temperaturethat allows CT−CS≦350 MPa (or |CT|−|CS|≦350 MPa) to be achieved when 10μm≦DOL_(short)≦40 μm. This permits an infinite increase of DOC withoutrisk of frangibility. Similarly, the frangibility criterion that storedelastic energy should be less than about 233 J/m²·mm and, in someembodiments, less than about 197 J/m²·mm, can be applied to a widevariety of glasses having DOC>0.1t, including Li₂O-rich glasses that mayhave Na⁺ for Li⁺ ion exchange, and also Na⁺ and K⁺ for Li⁺ ion exchange.In such instances, the criterion 10 μm≦DOL_(short)≦40 μm may be replacedwith a criterion 10 μm≦DOL_(short)≦40 μm, as DOL may not be defined inFSM-6000 terms.

FIG. 9 is a plot of the TE and TM refractive index profiles for of thedouble-ion-exchanged 0.55 mm thick glass sample shown in FIG. 8. For theK⁺ for Na⁺ ion exchange, the refractive index increases as a result ofthe ion exchange. The index profile is a monotonic function of depth,making it convenient to use IWKB analysis for the extraction andevaluation of stress profiles. The index profiles of FIG. 9 show that,in the case of double-ion-exchange (DIOX) profiles, the DOL estimated bythe FSM-6000 will significantly underestimate the chemical penetrationdepth for the deep region of the compressive layer and will not providedirect information about the steep shallow region, other thanapproximate estimate of the surface compressive stress. This is becausethe widely used DOL reported by FSM-6000 is calculated assuming that theindex profile is well represented by a single linear segment having asingle fixed slope and a single depth of penetration. The widely usedCT_(A) calculated based on that DOL and the surface CS is often a factorof two to three times greater than the physical CT for the DIOX profile,and is therefore not convenient to use as a predictor of frangibility.Thus, the analysis described in the present disclosure in terms ofphysical CT and stored elastic energy has a much broader realm ofapplication than the CT_(A)-based criteria of the prior art. TheDOL_(FSM) depth of layer for the present DIOX example is 75 μm, and theCT_(A) is about 167 MPa, which is more than twice the prior-art limit ofCT_(A)=CT₃(0.55)=80 MPa.

In some instances, stress profiles having large compression depth DOCmay be obtained using ion exchange such as, for example, during exchangeof Na⁺ for Li⁺ in a glass that is rich in Li₂O, that does not result inan increase of the. DOL based on measurement of the number of guidedoptical modes is not available in these cases. However, the compressiondepth DOC is a physical quantity that represents the depth of chemicalstrengthening can be measured by various polarimetry and refractivenear-field (RNF) techniques. As can be seen in Tables 3 and 4, the DOCis greater than 0.09t, usually exceeds 0.12t, and most often exceeds0.15t for the smaller thicknesses (t is the thickness) for allnon-frangible examples of glass with physical CT exceeding the prior-artfrangibility limit.

The criterion for non-frangibility, regardless of DOL, that is based onthe difference CT−CS can be equivalently restated as non-frangibilityregion for CT−CS<330 MPa, using a salt composition and temperature thatmay allow CT−CS values as high as 350 MPa when 10 μm≦DOL_(short)≦40 μm,thus allowing an infinite increase of DOC without risk of frangibility.Similarly, the frangibility criterion that stored elastic energy shouldbe <233 J/m2·mm, and, in some embodiments, less than about 197 J/m²·mmcan be applied to a wide variety of glasses having DOC>0.1t, includingLi₂O rich glasses that may have Na⁺ for Li⁺ ion exchange, and also Na⁺and K⁺ for Li⁺ ion exchange. In this case the criterion 10μm≦DOL_(short)≦40 μm may be replaced with a criterion 10μm≦DOC_(short)≦40 μm, as DOL may not be defined in terms of FSM-6000data.

In another embodiment, a frangibility criterion in the form of anormalized total energy is provided. The normalized total energy isdefined as:

$\begin{matrix}{W_{norm}^{tot} = {\frac{W_{el}^{tot}}{\left( \frac{1 - v}{E} \right)} = {\int_{0}^{Thickness}{\sigma^{2}\ {{x}.}}}}} & (24)\end{matrix}$

In many of the examples described above, when DOL>0.1t, particularlywhen the thickness is 0.4 mm, the fixed CT limit-based prediction offrangibility starts to become inaccurate. In these cases, the totalnormalized energy provides a better prediction of frangible behavior.While the total normalized energy values vary with the mechanicalparameters of the glass substrate, namely, the Poisson ration ν andYoung's modulus E, it is reasonable to assume that these values fall ina relatively compact range.

Therefore, in one embodiment, the ion exchanged glass article having acentral tension CT above the limit CT₃ for thicknesses less than orequal to 0.75 mm, or above the limit CT₁ for thicknesses greater than0.75 mm, has a total normalized elastic energy per unit thickness lessthan or equal to 37.5×10³ MPa² μm. For a thickness of 0.4 mm, asubstrate having a CT_(A) greater than 106.6 MPa should store anormalized elastic energy less than or equal to 15×10⁶ MPa² μm.

Depending on the glass composition and mechanical properties of theglass, the limits of the total normalized energy may change. However,these values fill the range of most of glasses of interest and encompassits practical limits where frangibility is avoided.

In another embodiment, the total normalized energy is less than 7.5×10⁶MPa² μm for 0.4 mm thick substrates. For other thicknesses, thenormalized stored elastic energy per unit thickness is less than about19×10³ MPa² μm.

The glass articles described herein may comprise or consist of any glassthat is chemically strengthened by ion exchange. In some embodiments,the glass is an alkali aluminosilicate glass.

In one embodiment, the alkali aluminosilicate glass comprises orconsists essentially of: at least one of alumina and boron oxide, and atleast one of an alkali metal oxide and an alkali earth metal oxide,wherein −15 mol %≦(R₂O+R′O−Al₂O₃−ZrO₂)−B₂O₃≦4 mol %, where R is one ofLi, Na, K, Rb, and Cs, and R′ is at least one of Mg, Ca, Sr, and Ba. Insome embodiments, the alkali aluminosilicate glass comprises or consistsessentially of: from about 62 mol % to about 70 mol.% SiO₂; from 0 mol %to about 18 mol % Al₂O₃; from 0 mol % to about 10 mol % B₂O₃; from 0 mol% to about 15 mol % Li₂O; from 0 mol % to about 20 mol % Na₂O; from 0mol % to about 18 mol % K₂O; from 0 mol % to about 17 mol % MgO; from 0mol % to about 18 mol % CaO; and from 0 mol % to about 5 mol % ZrO₂. Insome embodiments, the glass comprises alumina and boron oxide and atleast one alkali metal oxide, wherein −15 mol%≦(R₂O+R′O−Al₂O₃−ZrO₂)−B₂O₃≦4 mol %, where R is at least one of Li, Na,K, Rb, and Cs, and R′ is at least one of Mg, Ca, Sr, and Ba; wherein10≦Al₂O₃+B₂O₃+ZrO₂≦30 and 14≦R₂O+R′O≦25; wherein the silicate glasscomprises or consists essentially of: 62-70 mol.% SiO₂; 0-18 mol %Al₂O₃; 0-10 mol % B₂O₃; 0-15 mol % Li₂O; 6-14 mol % Na₂O; 0-18 mol %K₂O; 0-17 mol % MgO; 0-18 mol % CaO; and 0-5 mol % ZrO₂. The glass isdescribed in U.S. patent application Ser. No. 12/277,573 filed Nov. 25,2008, by Matthew J. Dejneka et al., and entitled “Glasses HavingImproved Toughness And Scratch Resistance,” and U.S. Pat. No. 8,652,978filed Aug. 17, 2012, by Matthew J. Dejneka et al., and entitled “GlassesHaving Improved Toughness And Scratch Resistance,” both claimingpriority to U.S. Provisional Patent Application No. 61/004,677, filed onNov. 29, 2008. The contents of all of the above are incorporated hereinby reference in their entirety.

In another embodiment, the alkali aluminosilicate glass comprises orconsists essentially of: from about 60 mol % to about 70 mol % SiO₂;from about 6 mol % to about 14 mol % Al₂O₃; from 0 mol % to about 15 mol% B₂O₃; from 0 mol % to about 15 mol % Li₂O; from 0 mol % to about 20mol % Na₂O; from 0 mol % to about 10 mol % K₂O; from 0 mol % to about 8mol % MgO; from 0 mol % to about 10 mol % CaO; from 0 mol % to about 5mol % ZrO₂; from 0 mol % to about 1 mol % SnO₂; from 0 mol % to about 1mol % CeO₂; less than about 50 ppm As₂O₃; and less than about 50 ppmSb₂O₃; wherein 12 mol %≦Li₂O+Na₂O+K₂O≦20 mol % and 0 mol %≦MgO+CaO≦10mol %. In some embodiments, the alkali aluminosilicate glass comprisesor consists essentially of: 60-70 mol % SiO₂; 6-14 mol % Al₂O₃; 0-3 mol% B₂O₃; 0-1 mol % Li₂O; 8-18 mol % Na₂O; 0-5 mol % K₂O; 0-2.5 mol % CaO;above 0 to 3 mol % ZrO₂; 0-1 mol % SnO₂; and 0-1 mol % CeO₂, wherein 12mol %<Li₂O+Na₂O+K₂O≦20 mol %, and wherein the silicate glass comprisesless than 50 ppm As₂O₃. In some embodiments, the alkali aluminosilicateglass comprises or consists essentially of: 60-72 mol % SiO₂; 6-14 mol %Al₂O₃; 0-3 mol % B₂O₃; 0-1 mol % Li₂O; 0-20 mol % Na₂O; 0-10 mol % K₂O;0-2.5 mol % CaO; 0-5 mol % ZrO₂; 0-1 mol % SnO₂; and 0-1 mol % CeO₂,wherein 12 mol %≦Li₂O+Na₂O+K₂O≦20 mol %, and wherein the silicate glasscomprises less than 50 ppm As₂O₃ and less than 50 ppm Sb₂O₃. The glassis described in U.S. Pat. No. 8,158,543 by Sinue Gomez et al., entitled“Fining Agents for Silicate Glasses,” filed on Feb. 25, 2009; U.S. Pat.No. 8,431,502 by Sinue Gomez et al., entitled “Silicate Glasses HavingLow Seed Concentration,” filed Jun. 13, 2012; and U.S. Pat. No.8,623,776, by Sinue Gomez et al., entitled “Silicate Glasses Having LowSeed Concentration,” filed Jun. 19, 2013, all of which claim priority toU.S. Provisional Patent Application No. 61/067,130, filed on Feb. 26,2008. The contents of all of the above are incorporated herein byreference in their entirety.

In another embodiment, the alkali aluminosilicate glass comprises SiO₂and Na₂O, wherein the glass has a temperature T_(35kp) at which theglass has a viscosity of 35 kilo poise (kpoise), wherein the temperatureT_(breakdown) at which zircon breaks down to form ZrO₂ and SiO₂ isgreater than T_(35kp). In some embodiments, the alkali aluminosilicateglass comprises or consists essentially of: from about 61 mol % to about75 mol % SiO₂; from about 7 mol % to about 15 mol % Al₂O₃; from 0 mol %to about 12 mol % B₂O₃; from about 9 mol % to about 21 mol % Na₂O; from0 mol % to about 4 mol % K₂O; from 0 mol % to about 7 mol % MgO; and 0mol % to about 3 mol % CaO. The glass is described in U.S. patentapplication Ser. No. 12/856,840 by Matthew J. Dejneka et al., entitled“Zircon Compatible Glasses for Down Draw,” filed Aug. 10, 2010, andclaiming priority to U.S. Provisional Patent Application No. 61/235,762,filed on Aug. 29, 2009. The contents of the above are incorporatedherein by reference in their entirety.

In another embodiment, the alkali aluminosilicate glass comprises atleast 50 mol % SiO₂ and at least one modifier selected from the groupconsisting of alkali metal oxides and alkaline earth metal oxides,wherein [(Al₂O₃ (mol %)+B₂O₃(mol %))/(Σ alkali metal modifiers (mol%))]>1. In some embodiments, the alkali aluminosilicate glass comprisesor consists essentially of: from 50 mol % to about 72 mol % SiO₂; fromabout 9 mol % to about 17 mol % Al₂O₃; from about 2 mol % to about 12mol % B₂O₃; from about 8 mol % to about 16 mol % Na₂O; and from 0 mol %to about 4 mol % K₂O. In some embodiments, the glass comprises orconsists essentially of: at least 58 mol % SiO₂; at least 8 mol % Na₂O;from 5.5 to 12 mol % B₂O₃; and Al₂O₃, wherein [(Al₂O₃ (mol %)+B₂O₃(mol%))/(Σ alkali metal modifiers (mol %))]>1, Al₂O₃(mol %)>B₂O₃(mol %),0.9<R₂O/Al₂O₃<1.3. The glass is described in U.S. Pat. No. 8,586,492,entitled “Crack And Scratch Resistant Glass and Enclosures MadeTherefrom,” filed Aug. 18, 2010, by Kristen L. Barefoot et al., U.S.patent application Ser. No. 14/082,847, entitled “Crack And ScratchResistant Glass and Enclosures Made Therefrom,” filed Nov. 18, 2013, byKristen L. Barefoot et al., both claiming priority to U.S. ProvisionalPatent Application No. 61/235,767, filed on Aug. 21, 2009. The contentsof all of the above are incorporated herein by reference in theirentirety.

In another embodiment, the alkali aluminosilicate glass comprises SiO₂,Al₂O₃, P₂O₅, and at least one alkali metal oxide (R₂O), wherein0.75≦[(P₂O₅(mol %)+R₂O(mol %))/M₂O₃ (mol %)]≦1.2, where M₂O₃═Al₂O₃+B₂O₃.In some embodiments, the alkali aluminosilicate glass comprises orconsists essentially of: from about 40 mol % to about 70 mol % SiO₂;from 0 mol % to about 28 mol % B₂O₃; from 0 mol % to about 28 mol %Al₂O₃; from about 1 mol % to about 14 mol % P₂O₅; and from about 12 mol% to about 16 mol % R₂O; and, in certain embodiments, from about 40 toabout 64 mol % SiO₂; from 0 mol % to about 8 mol % B₂O₃; from about 16mol % to about 28 mol % Al₂O₃; from about 2 mol % to about 12% P₂O₅; andfrom about 12 mol % to about 16 mol % R₂O. The glass is described inU.S. patent application Ser. No. 13/305,271 by Dana C. Bookbinder etal., entitled “Ion Exchangeable Glass with Deep Compressive Layer andHigh Damage Threshold,” filed Nov. 28, 2011, and claiming priority toU.S. Provisional Patent Application No. 61/417,941, filed Nov. 30, 2010.The contents of all of the above are incorporated herein by reference intheir entirety.

In still another embodiment, the alkali aluminosilicate glass comprisesat least about 50 mol % SiO₂ and at least about 11 mol % Na₂O, and thecompressive stress is at least about 900 MPa. In some embodiments, theglass further comprises Al₂O₃ and at least one of B₂O₃, K₂O, MgO andZnO, wherein−340+27.1.Al₂O₃−28.7.B₂O₃+15.6.Na₂O−61.4.K₂O+8.1.(MgO+ZnO)≧0 mol %. Inparticular embodiments, the glass comprises or consists essentially of:from about 7 mol % to about 26 mol % Al₂O₃; from 0 mol % to about 9 mol% B₂O₃; from about 11 mol % to about 25 mol % Na₂O; from 0 mol % toabout 2.5 mol % K₂O; from 0 mol % to about 8.5 mol % MgO; and from 0 mol% to about 1.5 mol % CaO. The glass is described in U.S. patentapplication Ser. No. 13/533,298, by Matthew J. Dejneka et al., entitled“Ion Exchangeable Glass with High Compressive Stress,” filed Jun. 26,2012, and claiming priority to U.S. Provisional Patent Application No.61/503,734, filed Jul. 1, 2011. The contents of all of the above areincorporated herein by reference in their entirety.

In other embodiments, the alkali aluminosilicate glass is ionexchangeable and comprises: at least about 50 mol % SiO₂; at least about10 mol % R₂O, wherein R₂O comprises Na₂O; Al₂O₃; and B₂O₃, whereinB₂O₃−(R₂O−Al₂O₃)≧3 mol %. In some embodiments, the glass comprises: atleast about 50 mol % SiO₂; at least about 10 mol % R₂O, wherein R₂Ocomprises Na₂O; Al₂O₃, wherein Al₂O₃(mol %)<R₂O(mol %); and 3-4.5 mol %B₂O₃, wherein B₂O₃(mol %)−(R₂O(mol %)−Al₂O₃(mol %))≧3 mol %. In certainembodiments, the glass comprises or consists essentially of: at leastabout 50 mol % SiO₂; from about 9 mol % to about 22 mol % Al₂O₃; fromabout 3 mol % to about 10 mol % B₂O₃; from about 9 mol % to about 20 mol% Na₂O; from 0 mol % to about 5 mol % K₂O; at least about 0.1 mol % MgO,ZnO, or combinations thereof, wherein 0≦MgO≦6 and 0≦ZnO≦6 mol %; and,optionally, at least one of CaO, BaO, and SrO, wherein 0 mol%≦CaO+SrO+BaO≦2 mol %. When ion exchanged, the glass, in someembodiments, has a Vickers crack initiation threshold of at least about10 kgf. Such glasses are described in U.S. patent application Ser. No.14/197,658, filed May 28, 2013, by Matthew J. Dejneka et al., entitled“Zircon Compatible, Ion Exchangeable Glass with High Damage Resistance,”which is a continuation of U.S. patent application Ser. No. 13/903,433,filed May 28, 2013, by Matthew J. Dejneka et al., entitled “ZirconCompatible, Ion Exchangeable Glass with High Damage Resistance,” bothclaiming priority to Provisional Patent Application No. 61/653,489,filed May 31, 2012. The contents of these applications are incorporatedherein by reference in their entirety.

In some embodiments, the glass comprises: at least about 50 mol % SiO₂;at least about 10 mol % R₂O, wherein R₂O comprises Na₂O; Al₂O₃, wherein−0.5 mol %≦Al₂O₃(mol %)−R₂O(mol %)≦2 mol %; and B₂O₃, and whereinB₂O₃(mol %)−(R₂O(mol %)−Al₂O₃(mol %))≧4.5 mol %. In other embodiments,the glass has a zircon breakdown temperature that is equal to thetemperature at which the glass has a viscosity of greater than about 40kPoise and comprises: at least about 50 mol % SiO₂; at least about 10mol % R₂O, wherein R₂O comprises Na₂O; Al₂O₃; and B₂O₃, wherein B₂O₃(mol%)−(R₂O(mol %)−Al₂O₃(mol %))≧4.5 mol %. In still other embodiments, theglass is ion exchanged, has a Vickers crack initiation threshold of atleast about 30 kgf, and comprises: at least about 50 mol % SiO₂; atleast about 10 mol % R₂O, wherein R₂O comprises Na₂O; Al₂O₃, wherein−0.5 mol %≦Al₂O₃(mol %)−R₂O(mol %)≦2 mol %; and B₂O₃, wherein B₂O₃(mol%)−(R₂O(mol %)−Al₂O₃(mol %))≧4.5 mol %. Such glasses are described inU.S. Pat. No. 903,398, by Matthew J. Dejneka et al., entitled “IonExchangeable Glass with High Damage Resistance,” filed May 28, 2013,claiming priority from U.S. Provisional Patent Application No.61/653,485, filed May 31, 2012. The contents of these applications areincorporated by reference herein in their entirety.

In certain embodiments, the alkali aluminosilicate glass comprises atleast about 4 mol % P₂O₅, wherein (M₂O₃(mol %)/R_(x)O (mol %))<1,wherein M₂O₃═Al₂O₃+B₂O₃, and wherein R_(x)O is the sum of monovalent anddivalent cation oxides present in the alkali aluminosilicate glass. Insome embodiments, the monovalent and divalent cation oxides are selectedfrom the group consisting of Li₂O, Na₂O, K₂O, Rb₂O, Cs₂O, MgO, CaO, SrO,BaO, and ZnO. In some embodiments, the glass comprises 0 mol % B₂O₃. Insome embodiments, the glass is ion exchanged to a depth of layer of atleast about 10 μm and comprises at least about 4 mol % P₂O₅, wherein0.6<[M₂O₃(mol %)/R_(x)O (mol %)]<1.4; or 1.3<[(P₂O₅+R₂O)/M₂O₃]≦2.3;where M₂O₃═Al₂O₃+B₂O₃, R_(x)O is the sum of monovalent and divalentcation oxides present in the alkali aluminosilicate glass, and R₂O isthe sum of divalent cation oxides present in the alkali aluminosilicateglass. The glass is described in U.S. patent application Ser. No.13/678,013 by Timothy M. Gross, entitled “Ion Exchangeable Glass withHigh Crack Initiation Threshold,” filed Nov. 15, 2012, and U.S. patentapplication Ser. No. 13/677,805 by Timothy M. Gross, entitled “IonExchangeable Glass with High Crack Initiation Threshold,” filed Nov. 15,2012, both claiming priority to U.S. Provisional Patent Application No.61/560,434 filed Nov. 16, 2011. The contents of these applications areincorporated herein by reference in their entirety.

In other embodiments, the alkali aluminosilicate glass comprises: fromabout 50 mol % to about 72 mol % SiO₂; from about 12 mol % to about 22mol % Al₂O₃; up to about 15 mol % B₂O₃; up to about 1 mol % P₂O₅; fromabout 11 mol % to about 21 mol % Na₂O; up to about 5 mol % K₂O; up toabout 4 mol % MgO; up to about 5 mol % ZnO; and up to about 2 mol % CaO.In some embodiments, the glass comprises: from about 55 mol % to about62 mol % SiO₂; from about 16 mol % to about 20 mol % Al₂O₃; from about 4mol % to about 10 mol % B₂O₃; from about 14 mol % to about 18 mol %Na₂O; from about 0.2 mol % to about 4 mol % K₂O; up to about 0.5 mol %MgO; up to about 0.5 mol % ZnO; and up to about 0.5 mol % CaO, whereinthe glass is substantially free of P₂O₅. In some embodiments,Na₂O+K₂O—Al₂O₃≦2.0 mol % and, in certain embodiments, Na₂O+K₂O−Al₂O₃≦0.5mol %. In some embodiments, B₂O₃—(Na₂O+K₂O−Al₂O₃)>4 mol % and, incertain embodiments, B₂O₃—(Na₂O+K₂O−Al₂O₃)>1 mol %. In some embodiments,24 mol %≦RAlO₄≦45 mol %, and, in other embodiments, 28 mol %≦RAlO₄≦45mol %, where R is at least one of Na, K, and Ag. The glass is describedin U.S. Provisional Patent Application No. 61/909,049 by Matthew J.Dejneka et al., entitled “Fast Ion Exchangeable Glasses with HighIndentation Threshold,” filed Nov. 26, 2013, the contents of which areincorporated herein by reference in their entirety.

In some embodiments, the glasses described herein are substantially freeof at least one of arsenic, antimony, barium, strontium, bismuth,lithium, and their compounds. In other embodiments, the glasses mayinclude up to about 5 mol % Li₂O and, in some embodiments, up to about10 mol % Li₂O.

In some embodiments, the glasses described herein, when ion exchanged,are resistant to introduction of flaws by sharp or sudden impact.Accordingly, these ion exchanged glasses exhibit Vickers crackinitiation threshold of at least about 10 kilogram force (kgf). Incertain embodiments, these glasses exhibit a Vickers crack initiationthreshold of at least 20 kgf and, in some embodiments, at least about 30kgf.

The glasses described herein may, in some embodiments, be down-drawableby processes known in the art, such as slot-drawing, fusion drawing,re-drawing, and the like, and have a liquidus viscosity of at least 130kilopoise. In addition to those compositions listed hereinabove, variousother ion exchangeable alkali aluminosilicate glass compositions may beused.

While typical embodiments have been set forth for the purpose ofillustration, the foregoing description should not be deemed to be alimitation on the scope of the disclosure or appended claims.Accordingly, various modifications, adaptations, and alternatives mayoccur to one skilled in the art without departing from the spirit andscope of the present disclosure or appended claims.

1. A glass having a compressive layer extending from a surface of theglass to a depth of compression DOC and under a maximum compressivestress CS, a central region having a maximum physical central tension CTat a center of the glass, the central region extending outward from thecenter to the depth of compression, and a thickness t in a range fromabout 0.3 mm to about 1.0 mm, wherein DOC≧0.08·t and CT−CS≦350 MPa. 2.The glass of claim 1, wherein the glass exhibits non-frangible behaviorwhen the surface having the compressive layer is subjected to a pointimpact force sufficient to create at least one new crack at the surfaceand extend the crack through the compressive layer to the centralregion.
 3. The glass of claim 2, wherein the glass has a frangibilityindex of less than
 3. 4. The glass of claim 2, wherein CT_(A) is thecentral tension CT as determined by FSM, whereinCT_(A)(MPa)=CT₁≧57(MPa)−9.0(MPa)·ln(t)+49.3(MPa)·ln²(t)(mm) when thethickness t is less than or equal to 0.75 mm, and wherein CT_(A) andwherein CT_(A)=CT₃≧−38.7(MPa)×ln(t)+48.2(MPa) when t is greater than0.75 mm.
 5. The glass of claim 1, wherein DOC≧0.09·t and the thickness tis greater than 0.5 mm.
 6. The glass of claim 1, wherein DOC≧0.1·t. 7.The glass of claim 6, wherein DOC≧0.15·t.
 8. The glass of claim 1,wherein the thickness t is greater than 0.75 mm.
 9. The glass of claim1, wherein the glass has an average elastic energy density of less than200 J/m²·mm.
 10. The glass of claim 9, wherein the glass has an averageelastic energy density of less than 140 J/m²·mm.
 11. The glass of claim10, wherein the glass has an average elastic energy density of less than120 J/m²·mm.
 12. The glass of claim 1, wherein the glass is strengthenedby ion exchange.
 13. The glass of claim 12, wherein the compressivestress CS is at least about 150 MPa.
 14. The glass of claim 12, whereinthe compressive stress CS is less than about 250 MPa.
 15. The glass ofclaim 1, wherein CT−CS≦334 MPa.
 16. The glass of claim 1, the glass hasa total normalized elastic energy less than or equal to 37.5×10³ MPa²μm.
 17. The glass of claim 1, wherein the thickness t is 0.4 mm andwherein the glass has a normalized elastic energy less than or equal to15×10⁶ MPa² μm.
 18. The glass of claim 17, wherein the normalized storedelastic energy per unit thickness is less than about 19×10³ MPa² μm. 19.The glass of claim 1, wherein the glass is an alkali aluminosilicateglass.
 20. The glass of claim 19, wherein the alkali aluminosilicateglass comprises: from about 60 mol % to about 70 mol % SiO₂; from about6 mol % to about 14 mol % Al₂O₃; from 0 mol % to about 15 mol % B₂O₃;from 0 mol % to about 15 mol % Li₂O; from 0 mol % to about 20 mol %Na₂O; from 0 mol % to about 10 mol % K₂O; from 0 mol % to about 8 mol %MgO; from 0 mol % to about 10 mol % CaO; from 0 mol % to about 5 mol %ZrO₂; from 0 mol % to about 1 mol % SnO₂; from 0 mol % to about 1 mol %CeO₂; less than about 50 ppm As₂O₃; and less than about 50 ppm Sb₂O₃;wherein 12 mol %≦Li₂O+Na₂O+K₂O≦20 mol % and 0 mol %≦MgO+CaO≦10 mol %.21. The glass of claim 19, wherein the alkali aluminosilicate glasscomprises: at least about 50 mol % SiO₂; at least about 10 mol % R₂O,wherein R₂O comprises Na₂O; Al₂O₃, wherein −0.5 mol %≦Al₂O₃(mol%)−R₂O(mol %)≦2 mol %; and B₂O₃, and wherein B₂O₃(mol %)−(R₂O(mol%)−Al₂O₃(mol %))≧4.5 mol %.
 22. The glass of claim 19, wherein thealkali aluminosilicate glass comprises: the alkali aluminosilicate glassis ion exchangeable and comprises: at least about 50 mol % SiO₂; atleast about 10 mol % R₂O, wherein R₂O comprises Na₂O; Al₂O₃; and B₂O₃,wherein B₂O₃−(R₂O−Al₂O₃)≧3 mol %.
 23. The glass of claim 19, wherein thealkali aluminosilicate glass comprises at least about 4 mol % P₂O₅ andfrom 0 mol % to about 4 mol % B₂O₃, and wherein1.3<[(P₂O₅+R₂O)/M₂O₃]≦2.3, where M₂O₃═Al₂O₃+B₂O₃, and R₂O is the sum ofmonovalent cation oxides present in the alkali aluminosilicate glass.24. The glass of claim 19, wherein the alkali aluminosilicate glasscomprises: from about 50 mol % to about 72 mol % SiO₂; from about 12 mol% to about 22 mol % Al₂O₃; up to about 15 mol % B₂O₃; up to about 1 mol% P₂O₅; from about 11 mol % to about 21 mol % Na₂O; up to about 5 mol %K₂O; up to about 4 mol % MgO; up to about 5 mol % ZnO; and up to about 2mol % CaO, wherein Na₂O+K₂O−Al₂O₃≦2.0 mol %, B₂O₃−(Na₂O+K₂O−Al₂O₃)>4 mol%, and 24 mol %≦RAlO₄≦45 mol %.
 25. The glass of claim 19, wherein thealkali aluminosilicate glass further comprises up to about 10 mol %Li₂O.
 26. The glass of claim 19, wherein the glass is substantially freeof lithium.
 27. A glass having a compressive layer extending from asurface of the glass to a depth of compression DOC and under a maximumcompressive stress CS, a central region having a maximum physicalcentral tension CT at a center of the glass, the central regionextending outward from the center to the depth of compression into theglass, and a thickness t in a range from about 0.3 mm to about 1.0 mm,wherein: a. the depth of compression DOC is greater than or equal to0.08·t; and b. the glass has an average elastic energy density of lessthan about 200 J/m²·mm.
 28. The glass of claim 27, wherein the glassexhibits non-frangible behavior when the surface having the compressivelayer is subjected to a point impact force sufficient to create at leastone new crack at the surface and extend the crack through thecompressive layer.
 29. The glass of claim 28, wherein the glass has afrangibility index of less than
 3. 30. The glass of claim 27, whereinCT_(A) is the central tension CT as determined by FSM, whereinCT_(A)(MPa)=CT₁≧57(MPa)−9.0(MPa)·ln(t)+49.3(MPa)·ln²(t)(mm) when thethickness t is less than or equal to 0.75 mm, and wherein CT_(A) andwherein CT_(A)=CT₃≧−38.7(MPa)×ln(t)+48.2(MPa) when t is greater than0.75 mm.
 31. The glass of claim 27, wherein the thickness t is greaterthan 0.75 mm.
 32. The glass of claim 31, wherein the glass has anaverage elastic energy density of less than 140 J/m²·mm.
 33. The glassof claim 32, wherein the glass has an average elastic energy density ofless than 120 J/m²·mm.
 34. The glass of claim 27, wherein the glass isstrengthened by ion exchange.
 35. The glass of claim 34, wherein thecompressive stress CS is at least about 150 MPa.
 36. The glass of claim35, wherein the compressive stress CS is less than about 250 MPa. 37.The glass of claim 27, wherein CT−CS≦334 MPa.
 38. The glass of claim 27,wherein the glass is an alkali aluminosilicate glass.
 39. The glass ofclaim 38, wherein the alkali aluminosilicate glass comprises: from about60 mol % to about 70 mol % SiO₂; from about 6 mol % to about 14 mol %Al₂O₃; from 0 mol % to about 15 mol % B₂O₃; from 0 mol % to about 15 mol% Li₂O; from 0 mol % to about 20 mol % Na₂O; from 0 mol % to about 10mol % K₂O; from 0 mol % to about 8 mol % MgO; from 0 mol % to about 10mol % CaO; from 0 mol % to about 5 mol % ZrO₂; from 0 mol % to about 1mol % SnO₂; from 0 mol % to about 1 mol % CeO₂; less than about 50 ppmAs₂O₃; and less than about 50 ppm Sb₂O₃; wherein 12 mol%≦Li₂O+Na₂O+K₂O≦20 mol % and 0≦mol % MgO+CaO≦10 mol %.
 40. The glass ofclaim 38, wherein the alkali aluminosilicate glass comprises: at leastabout 50 mol % SiO₂; at least about 10 mol % R₂O, wherein R₂O comprisesNa₂O; Al₂O₃, wherein −0.5 mol %≦Al₂O₃(mol %)−R₂O(mol %)≦2 mol %; andB₂O₃, and wherein B₂O₃(mol %)−(R₂O(mol %)−Al₂O₃(mol %))≧4.5 mol %. 41.The glass of claim 38, wherein the alkali aluminosilicate glasscomprises: the alkali aluminosilicate glass is ion exchangeable andcomprises: at least about 50 mol % SiO₂; at least about 10 mol % R₂O,wherein R₂O comprises Na₂O; Al₂O₃; and B₂O₃, wherein B₂O₃−(R₂O−Al₂O₃)≧3mol %.
 42. The glass of claim 38, wherein the alkali aluminosilicateglass comprises at least about 4 mol % P₂O₅ and from 0 mol % to about 4mol % B₂O₃, and wherein 1.3<[(P₂O₅+R₂O)/M₂O₃]≦2.3, whereM₂O₃═Al₂O₃+B₂O₃, and R₂O is the sum of monovalent cation oxides presentin the alkali aluminosilicate glass.
 43. The glass of claim 38, whereinthe alkali aluminosilicate glass comprises: from about 50 mol % to about72 mol % SiO₂; from about 12 mol % to about 22 mol % Al₂O₃; up to about15 mol % B₂O₃; up to about 1 mol % P₂O₅; from about 11 mol % to about 21mol % Na₂O; up to about 5 mol % K₂O; up to about 4 mol % MgO; up toabout 5 mol % ZnO; and up to about 2 mol % CaO, whereinNa₂O+K₂O−Al₂O₃≦2.0 mol %, B₂O₃−(Na₂O+K₂O−Al₂O₃)>4 mol %, and 24 mol%≦RAlO₄≦45 mol %.
 44. The glass of claim 38, wherein the alkalialuminosilicate glass further comprises up to about 10 mol % Li₂O. 45.The glass of claim 38, wherein the glass is substantially free oflithium.
 46. A glass, the glass comprising: a. a compressive layerextending from a surface of the glass to a depth of compression DOC, thecompressive surface layer having a maximum compressive stress CS; b. acentral region having a maximum physical central tension CT at a centerof the glass, the central region extending outward from the center ofthe glass to the depth of compression; c. a thickness t in a range fromabout 0.3 mm to about 1.0 mm, wherein DOC≧0.08·t and CT−CS≦350 MPa; andwherein: i. the physical central tension CT is greater than0.681×(57−9.0×ln(t)+49.3×(ln(t))²) when 0.3 mm≦t≦0.5 mm; ii. thephysical central tension CT is greater than0.728×(57−9.0×ln(t)+49.3×(ln(t))²) when 0.5 mm≦t≦0.7 mm; and iii. thephysical central tension CT is greater than$0.755 \times \left( {{{- 38.7}\left( \frac{MPa}{mm} \right) \times {\ln (t)}({mm})} + {48.2({MPa})}} \right)$when 0.7 mm<t≦1.0 mm.
 47. The glass of claim 46, wherein: a. thephysical central tension CT is greater than0.728×(57−9.0×ln(t)+49.3×(ln(t))²) when 0.3 mm≦t≦0.5 mm; b. the physicalcentral tension CT is greater than 0.751×(57−9.0×ln(t)+49.3×(ln(t))²)when 0.5 mm≦t≦0.7 mm; and c. the physical central tension CT is greaterthan$0.768 \times \left( {{{- 38.7}\left( \frac{MPa}{mm} \right) \times {\ln (t)}({mm})} + {48.2({MPa})}} \right)$when 0.7 mm<t≦1.0 mm.
 48. The glass of claim 46, wherein the glass hasan average elastic energy density of less than 200 J/m²·mm.
 49. Theglass of claim 48, wherein the glass has an average elastic energydensity of less than 140 J/m²·mm.
 50. The glass of claim 49, wherein theglass has an average elastic energy density of less than 120 J/m²·mm.51. The glass of claim 46, wherein the compressive stress CS is at leastabout 150 MPa.
 52. The glass of claim 35, wherein the compressive stressCS is less than about 250 MPa.
 53. The glass of claim 46, wherein theglass is an alkali aluminosilicate glass.
 54. The glass of claim 46,wherein the glass is an alkali aluminosilicate glass.
 55. A glass, theglass comprising: a. a compressive layer extending from a surface of theglass to a depth of compression DOC, the compressive surface layerhaving a maximum compressive stress CS; b. a central region having amaximum physical central tension CT at a center of the glass, thecentral region extending outward from the center of the glass to thedepth of compression, wherein the glass has an average elastic energydensity of less than 200 J/m²·mm; c. a thickness t in a range from about0.3 mm to about 1.0 mm, wherein DOC≧0.08·t and; and wherein: i. thephysical central tension CT is greater than0.681×(57−9.0×ln(t)+49.3×(ln(t))²) when 0.3 mm≦t≦0.5 mm; ii. thephysical central tension CT is greater than0.728×(57−9.0×ln(t)+49.3×(ln(t))²) when 0.5 mm≦t≦0.7 mm; and iii. thephysical central tension CT is greater than$0.755 \times \left( {{{- 38.7}\left( \frac{MPa}{mm} \right) \times {\ln (t)}({mm})} + {48.2({MPa})}} \right)$when 0.7 mm<t≦1.0 mm.
 56. The glass of claim 46, wherein: a. thephysical central tension CT is greater than0.728×(57−9.0×ln(t)+49.3×(ln(t))²) when 0.3 mm≦t≦0.5 mm; b. the physicalcentral tension CT is greater than 0.751×(57−9.0×ln(t)+49.3×(ln(t))²)when 0.5 mm≦t≦0.7 mm; and c. the physical central tension CT is greaterthan$0.768 \times \left( {{{- 38.7}\left( \frac{MPa}{mm} \right) \times {\ln (t)}({mm})} + {48.2({MPa})}} \right)$when 0.7 mm<t≦1.0 mm.
 57. The glass of claim 48, wherein the glass hasan average elastic energy density of less than 140 J/m²·mm.
 58. Theglass of claim 49, wherein the glass has an average elastic energydensity of less than 120 J/m²·mm.
 59. The glass of claim 27, wherein theglass is strengthened by ion exchange.
 60. The glass of claim 34,wherein the compressive stress CS is at least about 150 MPa.
 61. Theglass of claim 35, wherein the compressive stress CS is less than about250 MPa.
 62. The glass of claim 27, wherein the glass is an alkalialuminosilicate glass.